text:
\section{Introduction}

	Since the early studies of G\"{o}rtler~\cite{gortler1943} and Mowbray \& Rarity~\cite{mowbray1967b}, laboratory experiments have played a central role in the development of understanding of internal wave fields. Initially, much of the focus was on two-dimensional internal wave beams generated by excitation methods such as an oscillating cylinder~\cite{mowbray1967b, sutherland1999} or moving topography~\cite{aguilar2006, echeverri2009}. For modeling purposes, such a wave field can be treated as nominally invariant in the transverse direction and thus described in terms of plane waves \textit{via} Fourier transforms~\cite{lighthill1967, sutherland2010}.

	Inspired by oceanographic considerations, and building on earlier experiments that utilized paddle generators to excite vertical~\cite{cacchione1974} or horizontal~\cite{thorpe1968a, thorpe1968b} modes, more recently, novel internal wave generator technology~\cite{gostiaux2006} has been utilized for a variety of studies of two-dimensional internal wave modes. In doubly-confined geometries (i.e. sidewalls, top and bottom), two-dimensional modes of different orders, determined by the combination of stratification, imposed frequency and dimensions of confinement, have been studied~\cite{benielli1998, sutherland2010}. The capability of the novel generator technology to investigate wave beams and two-dimensional modes was thoroughly explored by Mercier \textit{et al}~\cite{mercier2017}. Such capabilities have been employed to investigate, for example, the Triadic Resonant Instability (TRI) in a vertical mode propagating horizontally~\cite{joubaud2012} or the formation of multilayered stratifications~\cite{dossmann2017}. While theoretical studies for linear stratifications describe such wave fields in terms of the natural modal basis of sines and cosines, it should be recalled that the modal pattern can be considered as a combination of plane waves propagating and reflecting from the system boundaries~\cite{mercier2017}.

	Axisymmetric wave fields have traditionally been experimentally excited using an oscillating sphere and exploring the shape of the wave beams~\cite{ermanyuk2011, flynn2003, ghaemsaidi2013, mowbray1967a, peacock2005, stevenson1969}. While the form of the wave field close to the oscillating body is nontrivial, modeling studies have explored the limit states of the wave beams in terms of plane waves with a spherical amplitude decreasing as $r^{-1/2}$, $r$ being the radial distance from the sphere, computed from the Green function of the moving source~\cite{voisin2003}, or as infinite sums of Bessel functions with complex coefficients~\cite{davis2010, sutherland2010}.  The amplitude decrease and the viscous decay of the conical wave beam emitted by an oscillating sphere has been explored in laboratory experiments by Flynn \textit{et al}~\cite{flynn2003} showing good agreement with theoretical predictions. More sophisticated axisymmetric experimental geometries have been investigated using a vertically oscillating torus~\cite{duranmatute2013, ermanyuk2017}, in which case a highly non-linear process occurs due to the three-dimensional geometric focusing, able to transport momentum and break into turbulence. None of these experimental configurations, however, readily permitted a change in the form nor the wave number of the wave field being excited.

	An axisymmetric wave generator~\cite{maurer2017}, adapted from its planar counterpart~\cite{gostiaux2006}, has been demonstrated as capable of generating high-fidelity axisymmetric internal wave fields, with substantial flexibility in the setting of the radial wavelength. Studies using this technology reveal axisymmetric wave cones propagating in the stratified medium according to the internal wave dispersion relation and with radial profiles imposed by the configuration of the generator, such as ring-shaped excitation or truncated Bessel functions~\cite{maurer2017}. Wave amplitudes and frequencies were measured, showing a good agreement with the linear theory for axisymmetric waves in a stratified fluid of constant buoyancy, both in the non-rotating and rotating cases.

	To date, there have been no experimental studies of internal wave modes in an axisymmetric geometry. Furthermore, to our knowledge, there is no quantitative study of resonant confined modes, even in two-dimensional geometries. In this paper, we perform laboratory experimental realizations of axisymmetric modes, made possible by the new form of wave generator developed by Maurer \textit{et al}~\cite{maurer2017}. In section $2$ we establish the general theory for axisymmetric modes of internal waves by considering both radial and vertical confinement as well as weakly viscous effects. Then, in section $3$, we describe our experimental apparatus, adapted from Maurer's~\cite{maurer2017}. Experimental results are presented in section $4$, followed by conclusions and discussion in section $5$.

	\section{Theory}

		\subsection{Governing Equations}

		In a cylindrical framework ($\mathbf{e_r}$, $\mathbf{e_\theta}$, $\mathbf{e_z}$), with $\mathbf{e_z}$ the ascendent vertical, small amplitude inertia gravity waves in an inviscid rotating fluid with a constant background stratification satisfy the following equations in the Boussinesq approximation:
		\begin{align}
			\rho_0 \left(\dfrac{\partial \mathbf{v}}{\partial t} + \left(\mathbf{v}\cdot\mathbf{\nabla}\right) \mathbf{v}\right) &= - \rho_0 f \mathbf{e_z} \times \mathbf{v} - \mathbf{\nabla} p - (\rho - \bar{\rho}) g \mathbf{e_z},\label{eq:IW1}\\
			\dfrac{\partial \rho}{\partial t} + \left(\mathbf{v}\cdot \mathbf{\nabla}\right) \rho &= 0,\label{eq:IW2}\\
			\mathbf{\nabla} \cdot \mathbf{v} &= 0\label{eq:IW3},
		\end{align}
		where $\mathbf{v} = (v_r,~v_\theta,~v_z)$ is the velocity field, $p$ the pressure field, $\rho$ the density field, and $\bar{\rho}$ the background density field. We define the Coriolis frequency $f= 2 \Omega$ as twice the rotation frequency $\Omega$, and the buoyancy frequency $N$ \textit{via} the relation $N^2 = (-g/\rho_0) \partial \bar{\rho} / \partial z$ with $\rho_0$ being a reference density.

		Considering axisymmetric wave fields, we assume that there is no dependence in the orthoradial variable $\theta$ and hence all functions only depend on ($r$, $z$, $t$). By introducing the axisymmetric stream function $\psi$ such that:
		\begin{equation}
			v_r = - \frac{1}{r}\dfrac{\partial (r \psi)}{\partial z} \mathrm{~~~~~~~and~~~~~~~} v_z =\frac{1}{r}\dfrac{\partial (r \psi)}{\partial r},\label{eq:IW4}
		\end{equation}
		equations~\eqref{eq:IW1},~\eqref{eq:IW2}, and~\eqref{eq:IW3} become:
		\begin{align}
			\partial_t^2 \left(\partial_z^2 \psi + \partial_r \left(\frac{1}{r}\partial_r (r \psi) \right) \right) + N^2 \partial_r \left(\frac{1}{r}\partial_r (r\psi)\right) + f^2 \partial_z^2 \psi = 0.\label{eq:IW5}
		\end{align}
Natural axisymmetric solutions of this equation can be found through a Fourier-Hankel decomposition. Using a modal basis, the solutions write as linear combinations of Bessel functions of the first kind $J_1$ and of the second kind $Y_1$. They all lead to the same theoretical study, but $Y_1$ has a singularity at $r=0$ so only the $J_1$ function will be considered. As different radial wave numbers may enter in the decomposition, the stream function $\psi$ can then be written as a modal sum:
		\begin{equation}
			\psi (r,z,t) = \iint \phi (z) J_1 (l r) \exp (-i \omega t) \text{d} l \text{d} \omega.\label{eq:IW6}
		\end{equation}

		Radial and vertical velocities can be derived from equation~\eqref{eq:IW6} using classic relations for the Bessel derivatives, as follows:
		\begin{align}
			v_r &= \iint \phi'(z) J_1(lr) \exp(-i \omega t) \text{d} l \text{d} \omega, \label{eq:IW7}\\
			v_z &= \iint l \phi(z) J_0(lr) \exp(-i \omega t) \text{d} l \text{d} \omega.\label{eq:IW8}
		\end{align}
For a given frequency $\omega$ and radial mode $l$, $\phi(z)$ satisfies:
		\begin{equation}
			(f^2 - \omega^2) \phi'' (z) -l^2 (N^2 - \omega^2) \phi (z) = 0.\label{eq:IW9}
		\end{equation}
Solutions of equation~\eqref{eq:IW9} are exponential functions, either complex or real. They can be either propagative or evanescent waves, depending on the frequency, as long as the vertical wave number $m$ satisfies the dispersion relation:
		\begin{equation}
			m^2 =  l^2 \frac{N^2 - \omega^2}{\omega^2 - f^2}.\label{eq:IW10}
		\end{equation}

		The effect of rotation on a conical wave beam emitted in a stratified fluid has already been documented in previous studies~\cite{maurer2017, peacock2005}. Hence, results for gravity waves could be easily extended to a rotating case with inertial or, more generally, inertia-gravity waves, as it mainly changes the vertical wave number $m$. In this study, we focus on a non-rotating fluid ($f=0$). The dispersion relation simplifies and if we define $\beta = \sin ^{-1} (l/k)$ to be the angle between the vertical axis and the wave vector $\mathbf{k}=(l,0,m)$, we obtain:
		\begin{equation}
			\sin \beta = \pm \frac{\omega}{N}.\label{eq:IW11}
		\end{equation}
According to equation~\eqref{eq:IW11}, internal gravity waves propagate along a direction fixed by the angle $\beta$. In a two dimensional geometry, four wave beams on a St Andrew's Cross are formed~\cite{mowbray1967b, sutherland1999}. In a three dimensional axisymmetric geometry, the dispersion relation sets two cones aligned along the vertical direction and connected by the apex~\cite{peacock2005, sutherland2010}.

		\subsection{Radial Confinement}

		In a previous study, Maurer \textit{et al}~\cite{maurer2017} analysed the production of a conical wave field generated by an axisymmetric moving form at the surface, for which the radial profile was a truncated Bessel function. Although Bessel functions form a natural basis of study for axisymmetric wave fields, the analytical form of the wave field for a truncated Bessel function is not so simple. An illustration is presented in figure~\ref{fig:1}(a), which displays a vertical cut of the spatial structure of the wave field studied in~\cite{maurer2017}. Immediately below the generator (region $1$ in figure~\ref{fig:1}(a)), the wave field preserves its radial form, but further below the wave field develops a conical beam-shaped profile (region $2$), which can locally be modelled by a plane wave. Finally, due to the propagation angle set by~\eqref{eq:IW11}, sufficiently far below the oscillating body around the vertical axis the wave field is absent (region $3$). Analytically, this evolution of the wave field is a natural consequence of the truncated Bessel function forcing being expressed as an integral over Bessel functions of different wavelengths, with coefficients depending on the spatial forcing. Complex models have been set up to understand the nature of such radiated wave fields~\cite{davis2010, flynn2003, voisin2011}.
			\begin{figure}[!htbp]
				\centering
				\epsfig{file=fig1.eps}
				\caption{Left: beams for downwards propagating wave generation in an (a) unconfined and (b) confined geometries produced by a wave generator or an oscillating body (light grey rectangle). Right: (c) phase lines of two different wave beams allowed by the dispersion relation and (d) phase lines of the wave re-recombination for vertically propagating horizontal (radial) modes.}
				\label{fig:1}
			\end{figure}

		Given the finite spatial extent of the forcing, to generate a wave field of simple form expressible using a single radial Bessel function, confinement can be imposed experimentally to the fluid, as illustrated in figure~\ref{fig:1}(b). As for planar geometries, confinement prevents the wave from propagating in the bounded direction. Given the assumption of axisymmetry, we seek a wave field that is radially confined by a cylinder of radius $R$ equal to the radius of the generator, and vertically propagating, which is in contrast to the planar scenario that has vertical confinement and permits lateral propagation~\cite{dossmann2017, joubaud2012, mercier2017}. We impose the radial boundary condition:
		\begin{equation}
			v_r (r=R,z) = \left( \dfrac{\partial\psi}{\partial z}\right) _{(r=R, z)} = 0, \label{eq:IW12}
		\end{equation}
which corresponds to a maximum of vertical velocity and a vanishing radial velocity at the outer boundary, and conserves volume in the domain. Condition~\eqref{eq:IW12} limits possible values of the radial wave number $l$ and if the fluid is excited with this wavenumber at  frequency $\omega$, a single propagating mode is expected to result.

			Figure~\ref{fig:1}(c) shows the two directions of propagation allowed for the wave beams by the dispersion relation~\eqref{eq:IW11}, in a planar cross-section, for a wave generation at the surface. In our experiment, the radial confinement leads to downward propagating modes which are, as depicted in figure~\ref{fig:1}(c,d) (still in a planar cross-section) a re-combination of conically propagating beams. Due to the symmetry with respect to the vertical axis, the radial direction of propagation cancels out and, for a downwards propagating wave at a selected frequency $\omega$ and wavenumber $\mathbf{k}$, the phase and group velocities can be computed from the dispersion relation~\eqref{eq:IW11}:
		\begin{align}
			\mathbf{v_\phi} &= \frac{1}{2\pi} \int_0 ^{2\pi} \frac{N l}{k}(l \mathbf{e_r} + m \mathbf{e_z}) \text{d} \theta = \frac{N l m}{k}\mathbf{e_z},
			\label{eq:IW14a}\\
			\mathbf{v_g} &=  \frac{1}{2\pi} \int _0 ^{2\pi} \frac{m l N^2}{\omega k^4} (m\mathbf{e_r}-l\mathbf{e_z}) \text{d} \theta = - \frac{m l^2 N^2}{\omega k^4} \mathbf{e_z}.
			\label{eq:IW14b}
		\end{align}
		Equations~\eqref{eq:IW14a} and~\eqref{eq:IW14b} show phase and group velocity oriented in opposite directions, illustrated in figure~\ref{fig:1}(d), consistent with oceanic signatures identified by oceanographers looking for internal waves~\cite{alexander1995, alford2001}. This feature contrasts with horizontally propagating cartesian modes which show phase and group velocities pointing towards the same direction~\cite{mercier2017}.

			To investigate the shape of the wave field in the experimental domain, and more specifically its amplitude, we extend the axisymmetric analysis of Sutherland~\cite{sutherland2010}, first derived for an oscillating cylinder in a two-dimensional geometry, by applying it to our axisymmetric flat generator in a confined domain. Neglecting rotation, equation~\eqref{eq:IW5} can be rewritten:
			\begin{equation}
				\Gamma^2 \dfrac{\partial}{\partial r}\left(\frac{1}{r}\dfrac{\partial (r \psi)}{\partial r} \right) + \dfrac{\partial^2 \psi}{\partial z^2} = 0,\label{eq:IW15}
			\end{equation}
			with $\Gamma^2 = 1 -N^2/\omega^2$. Through a Fourier transform, the time dependency of the streamfunction can be expressed in complex coordinates as $\psi \propto e^{-i \omega t}$, the velocity field being the real part of the stream function derivatives.

			Considering that the plates of the generator are moving vertically and are injecting a vertical velocity $a \omega$, with $a$ being a sufficiently small displacement so that the fluid surface can be considered to reside at $z=0$, the boundary conditions that apply to the streamfunction field are:
			\begin{align}
				v_z (r, z=0) = \left(\frac{1}{r}\dfrac{\partial (r \psi)}{\partial r}\right)_{(r, z=0)} &= a \omega J_0 (l r), \label{eq:IW16}\\
				v_r (r=R,z) = \left( \dfrac{\partial\psi}{\partial z}\right) _{(r=R, z)} &= 0.\label{eq:IW17}
			\end{align}
			Equation~\eqref{eq:IW16} means that the generator imposes its own movement to the fluid at the top of the domain. The modal boundary condition is expressed by equation~\eqref{eq:IW17} as detailed before.

			For $N<\omega$, the problem can be readily solved \textit{via} a coordinate transformation: $(r' = \Gamma r,~z'=z)$ so that equation~\eqref{eq:IW15} becomes:
			\begin{equation}
				\Delta_h'\psi = 0,\label{eq:IW21}
			\end{equation}
			where $\Delta'_h$ is the horizontal Laplacian. The solution can be obtained using separation of variables. The radial part of the equation satisfies a Bessel differential equation of first order, leading to $\psi \propto J_1(l r)$. The vertical component is found to be exponential (see equation~\eqref{eq:IW9}), and $\psi \propto \exp(\Gamma l z)$ as the amplitude decreases as $z$ goes to $-\infty$. From the boundary conditions, the different coefficients can be set and recasting the solution in the original coordinates, we obtain:
			\begin{equation}
				\psi_{N<\omega} (r,z,t) = -\frac{a \omega}{l} J_1 (l r) \exp (m z) \cos (\omega t),\label{eq:IW22}
			\end{equation}
			where we define $m = \Gamma l$ as the vertical wave number, which contains the influence of the stratification.

			In the case $N > \omega$, the term $1 - N^2/ \omega^2$ is negative. We thus define $\gamma^2 = \omega^2/N^2 - 1$ and, by analytic continuation, the problem can be solved using the same method as before. Thanks to the second order derivatives, the problem keeps well-defined though we are using complex analysis and the final stream function belongs to the real space of functions:
			\begin{equation}
				\psi_{N>\omega} (r,z,t) = -\frac{a \omega}{l} J_1 (l r) \cos (m z - \omega t),\label{eq:IW23}
			\end{equation}
			with $m$ defined as $m^2 = - \gamma^2 l^2$. Hence, we obtain two different radial modes, one being evanescent~\eqref{eq:IW22} and the other one propagating in the vertical direction~\eqref{eq:IW23}.

			The vertical velocity being a radial derivative, it behaves as $v_z \propto a \omega$:
			\begin{align}
				v_z (r,z) = \frac{1}{r}\dfrac{\partial (r \psi)}{\partial r} &= a \omega J_0 (l r) \cos(mz -\omega t), \label{eq:IW40}\\
				v_r (r,z) = \dfrac{\partial\psi}{\partial z} &= -\frac{a \omega m}{l} J_1(l r) \sin(m z -\omega t).\label{eq:IW41}
			\end{align}

		\subsection{Vertical Confinement}

			Due to the finite extent of the experimental domain, boundaries at the top ($z=0$) and at the bottom ($z=-L$) are to be taken into account. This creates a cavity that behaves like an opto-electromagnetic cavity~\cite{jackson1999} or a Melde's string~\cite{melde1860}, with different modes and mechanical resonances. The total wave field in the cavity is obtained by a superposition of all the reflected waves, from the top and the bottom of the tank, creating constructive or destructive interferences. In this configuration, the generator is continuously exciting a velocity field of stream function $\psi_1$, written using the complex notation as:
			\begin{equation}
				\psi_1 (r, z, t) = \psi^0_1 J_1 (l r) e^{i(\omega t - m z)},\label{eq:IW27}
			\end{equation}
			with $\psi^0 = a \omega / l$. At $z=-L$, the downwards wave field $\psi_1$ is reflected into an upwards wave field $\psi_2$, and at $z=0$, the $\psi_2$ stream function is reflected into another downwards wave $\psi_3$. Repeated reflections occur at $z=0$ and $z=-L$, and as a result the total stream field is composed of an infinite sum of reflected wave fields.

			We denote by odd numbers the downwards waves and by even numbers the upwards waves. At the boundaries, as well as changing direction, reflection also induces a $\pi$ phase shift, and if we assume that there is no dissipation the amplitudes of the stream functions are equal before and after reflection. Boundary conditions at the top and at the bottom of the tank then apply as:
			\begin{align}
				\psi_{2k - 1} (z=-L) &= \psi_{2k} (z=-L) e^{i \pi}, \label{eq:IW28}\\
				\psi_{2k + 1} (z= 0) &= \psi_{2k} (z= 0) e^{i \pi}, \label{eq:IW29}
			\end{align}
			leading to:
			\begin{align}
				\psi^0_{2k} &= \psi^0_{2k - 1} e^{-2 i m L- i \pi}, \label{eq:IW30}\\
				\psi^0_{2k} &= \psi^0_{2k + 1} e^{i\pi}. \label{eq:IW31}
			\end{align}
We deduce that the general expression of these wave amplitudes are:
			\begin{align}
				\psi^0_{2k} &=  \psi^0_1 e^{-2ikmL + (2k-1)\pi}, \label{eq:IW32}\\
				\psi^0_{2k+1} &= \psi^0_1 e^{-2ikmL + (2k)\pi}. \label{eq:IW33}
			\end{align}
As the tank is filled by infinite wave reflections, we describe the total wave field by a sum over all the reflected waves:
			\begin{equation}
				\psi = \sum_{k=1}^\infty \psi_k = \psi^0_1 J_1 (l r) e^{i\pi / 2} e^{i \omega t} \frac{\sin (m(z - L))}{i \sin(mL)}, \label{eq:IW34}
			\end{equation}
			hence the real field becomes:
			\begin{equation}
				\Re (\psi) = \psi^0_1 J_1 (l r) \frac{\cos (\omega t) \sin (m(z-L))}{\sin (mL)}. \label{eq:IW35}
			\end{equation}

			Waves that contribute to the total wave field interact either constructively or destructively. In the first case, we would be able to define a temporal and a spatial period, fixed by the wave parameters $\omega$, $l$, and $m$, and by the size of the cavity $L$, as in any wave resonator. Exact cavity modes are obtained if the reflection at $z=-L$ produces a reflected wave in phase with the incoming wave, which means that this position is already a node of the wave field. This resonance condition can be expressed as:
			\begin{equation}
				L = n \frac{\lambda}{2}, \mathrm{~for~}n\in \mathbb{N},\label{eq:IW36}
			\end{equation}
			with $\lambda = 2\pi / m$ being the vertical spatial period. A direct consequence is that the reflection at $z=0$ also produces a wave in phase with the incoming wave, so all reflected waves will be interacting constructively. This relation can be written as a condition involving resonant frequencies $\omega_n$:
			\begin{equation}
				\frac{\omega_n}{N} = \frac{(L l)^2}{\pi^2 n^2 + (L l)^2}. \label{eq:IW39}
			\end{equation}
Similar to electromagnetic waves, the cavity operates as a frequency selector, as a discrete number of frequencies $\omega_n$ fulfills the resonance condition. We present in table~\ref{tab:resonantomegas} a list of the first ten resonant frequencies that can be selected in a radial mode$-1$ configuration with $L=60\mathrm{~cm}$ and $l=19\mathrm{~m^{-1}}$.
			\begin{table}[!htbp]
			\begin{center}
				\begin{tabular}{c c c c c c c c c c c c}
					\hline
					$n$ & $0$ & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & $9$ & $10$ \\
					\hline \hline
					$\omega_n / N$ & $1$ & $0,964$ & $0,876$ & $0,771$ & $0,672$ & $0,588$ & $0,518$ & $0,460$ & $0,413$ & $0,374$ & $0,341$ \\
					\hline
				\end{tabular}
				\caption{First ten resonant frequencies computed for $L=60\mathrm{~cm}$ and $l=19\mathrm{~m^{-1}}$.\label{tab:resonantomegas}}
			\end{center}
			\end{table}

			\subsection{Weakly Viscous Correction}

			In the preceding derivations, an inviscid fluid was assumed. This made possible the propagation of a single mode at all frequencies without damping effect, and the existence of exact resonant cavity modes. As we will see, however, such an approximation is only relevant for a selected range of frequencies. To quantify the viscous effects the wave propagation, we write the vertical wave number as the following expansion:
			\begin{equation}
				m = m_0 + i \varepsilon m_1 + \mathcal{O}(\varepsilon^2),\label{eq:IW24}
			\end{equation}
			with $\varepsilon = \nu l^2 / \omega$, $m_0$ being the inviscid wave number (equation~\eqref{eq:IW10}), and $m_1$ being the first order correction. Including viscous terms, equation~\eqref{eq:IW9} becomes:
			\begin{equation}
				\phi^{(4)}(z) - \left(2 l^2 + i \frac{f^2-\omega^2}{\nu \omega}\right) \phi ''(z) + l^2 \left(l^2 + i \frac{N^2 - \omega^2}{\nu \omega} \right)\phi(z) = 0. \label{eq:IW25}
			\end{equation}
			Hence, with the vertical dependence being $\exp(i m z)$ (complex notation of equation~\eqref{eq:IW23}) and $m$ defined as in equation~\eqref{eq:IW24}, one can extract from equation~\eqref{eq:IW25} the following weakly viscous correction:
			\begin{equation}
				i \varepsilon m_1 = \mp \frac{i \varepsilon l}{2 (1 - \gamma^2) \alpha^3\sqrt{1-\alpha^2}},
			\end{equation}
			where $\alpha = \omega /N$ and $\gamma = f/\omega$. For a non-rotating case, this correction simplifies to:
			\begin{equation}
				i \varepsilon m_1 = \mp \frac{i \varepsilon l }{2 \alpha^3\sqrt{1-\alpha^2}}.
			\end{equation}
			At an altitude $z$ below the wave generation source, the weakly viscous streamfunction $\psi_\nu$ writes:
			\begin{equation}
				\psi_\nu (z) = \psi (z) \exp (-\varepsilon m_1 |z|).\label{eq:IW26}
			\end{equation}

			According to equation~\eqref{eq:IW26}, the typical vertical length of viscous damping $1/\varepsilon m_1$ depends on the frequency $\omega$ and is much smaller at low frequencies than at high frequencies. Quantifying theoretically the viscous damping will help us to understand amplitudes observed in the tank when we compare them to the velocity amplitudes of the generator.

	\section{Experimental Apparatus}

		To conduct our experiments, the experimental setup of Maurer \textit{et al}~\cite{maurer2017} was adapted. A general schematic of the experimental apparatus is presented in figure~\ref{fig:fig2}. We introduce natural cylindric coordinates with $z$, the ascendent vertical at the center of the apparatus, and $r$ the radius orthogonal to the vertical axis. The origin in $z$ is taken at the surface of the water.

		The generator comprises sixteen, $1.2\mathrm{~cm}$ wide, concentric PVC cylinders periodically oscillating, each of them being forced by two eccentric cams. The eccentricities can be configured to introduce a phase shift between the different cylinders, and the oscillating amplitude can be set for each individual cylinder. As a result, the vertical displacement of the $n^{th}$ cylinder can be described by:
		\begin{equation}
			a_n(t) = A_n \cos (\omega t + \theta),
		\end{equation}
		with $A_n$ its amplitude, $\omega$ the forcing frequency, and $\theta$ a phase shift. For a smooth motion of the PVC cylinders, a $0.1\mathrm{~cm}$ gap is kept between each cylinder and the total diameter of the wave generator is then $40.2\mathrm{~cm}$. The generator is mounted at the surface of the water to force downwards internal waves.

				To investigate the ability of this experimental setup to produce modal wave fields, we set the generator in three different configurations to excite first, second, and third order modes. Modes are defined by the number of nodes of the Bessel function present in the range $r \in [0;~20]\mathrm{~cm}$ (size of the generator). It sets the radial wavelength and we computed the three associated wave numbers: $l_1=19\mathrm{~m^{-1}}$, $l_2=35\mathrm{~m^{-1}}$, and $l_3=51\mathrm{~m^{-1}}$. We did not look for modes of higher orders because the discretisation of the generator profile was not sufficient to produce smooth enough shapes of Bessel functions. The amplitudes of the different cams for the three modes are summarized in table~\ref{tab:shafts}. The profiles can be defined by the radial wavenumber $l$ and the amplitude at $r=0$ that we call $a$. The different amplitudes $a_n$, for $n\neq 0$, are taken to be the discrete approximation of the Bessel function defined by $l$ and $a$.
			\begin{table}[!htbp]
				\begin{center}
					\begin{tabular}{c c c c c c c c c c c c c c c c c}
						\hline
						Cams & $1$ & $2$ & $3$ & $4$ & $5$ & $6$ & $7$ & $8$ & $9$ & $10$ & $11$ & $12$ & $13$ & $14$ & $15$ & $16$ \\
						\hline \hline
						Mode$-1$ (high amplitude) & $5$ & $4.9$ & $4.7$ & $4.3$ & $3.9$ & $3.3$ & $2.6$ & $1.9$ & $1.2$ & $0.5$ & $-0.2$ & $-0.6$ & $-1.2$ & $-1.6$ & $-1.9$ & $-2$ \\
						Mode$-1$ (low amplitude)~ & $2.5$ & $2.4$ & $2.3$ & $2.1$ & $1.9$ & $1.6$ & $1.3$ & $0.9$ & $0.6$ & $0.2$ & $-0.1$ & $-0.3$ & $-0.6$ & $-0.8$ & $-0.9$ & $-1$ \\
						Mode$-2$ & $5$ & $4.7$ & $4$ & $2.9$ & $1.6$ & $0.3$ & $-0.8$ & $-1.6$ & $-2$ & $-1.9$ & $-1.5$ & $-0.9$ & $-0.1$ & $0.6$ & $1.2$ & $1.5$ \\
						Mode$-3$ & $5$ & $4.5$ & $3$ & $1.2$ & $-0.6$ & $-1.7$ & $-2$ & $-1.4$ & $-0.4$ & $0.7$ & $1.4$ & $1.5$ & $0.9$ & $0$ & $-0.8$ & $-1.2$ \\
						\hline
					\end{tabular}
					\caption{Amplitudes (in mm) of the different cams of the generator in the different mode profiles we used. The first cam is located at $r=0$.}
					\label{tab:shafts}
				\end{center}
			\end{table}

				Experiments were conducted in a cylindrical plexiglas tank of the same diameter as the generator to respect the boundary condition~\eqref{eq:IW12}. This transparent cylindrical tank was set into a square plexiglas tank to prevent the experiment visualisation suffering from optical deformations that would occur due to the curved interface created by the cylinder. Both tanks were filled with salt-stratified water with the same density profile. We used the double-bucket method to fill the tanks with a linear stratification~\cite{fortuin1960, oster1963}. Density and buoyancy as a function of depth were measured using a calibrated PME conductivity and temperature probe mounted on a motorized vertical axis. Buoyancy frequency is estimated from the mean value of the $N$ profile obtained from the density function $\rho(z)$. Errors on the buoyancy frequency are estimated using the standard deviation of this $N$ profile, and are in most cases about $4\%$ of the estimated $N$ value. We used buoyancy frequencies in the range $N~\approx~0.6\mathrm{~rad\cdot s^{-1}}$ to $N~\approx~1\mathrm{~rad\cdot s^{-1}}$.
		\begin{figure}[!htbp]
			\centering
			\epsfig{file=fig2.eps}
			\caption{Schematic of the experimental apparatus. Left: a cylindrical tank, inside a square tank, confines the waves produced by the generator located at the surface, leading to a radial Bessel mode propagating downwards. Right: idealised linear stratification and constant buoyancy frequency.}
			\label{fig:fig2}
		\end{figure}

		Velocity fields were obtained via Particle Image Velocimetry (PIV). A laser sheet was created by a laser beam (Ti:Sapphire, $2\mathrm{~watts}$, wavelength $532\mathrm{~nm}$) going through a cylindrical lens. It could be oriented either horizontally (to measure the radial and orthoradial velocity) or vertically (to measure the vertical and the radial velocity). For the purpose of visualisation, $10\mathrm{~\mu m}$ diameter hollow glass spheres of volumetric mass $1.1\mathrm{~kg\cdot L^{-1}}$ were added to the fluid while filling the tank. To get good quality velocity fields at the bottom of the tank and while imaging in a horizontal plane, $10\mathrm{~\mu m}$ silver-covered spheres of volumetric mass $1.4\mathrm{~kg\cdot L^{-1}}$ were added when needed in some experiments. Images were recorded at $1\mathrm{~Hz}$ and data processing of the PIV raw images was done using the CIVx algorithm~\cite{fincham2000}.

	\section{Results}

		\subsection{Radial Modes}

			Figure~\ref{fig:fig3} presents a summary of the experimental PIV results for the generation of modes $1$ through $3$ in a linear stratification with $\omega/N = 0.6$ for modes $1$ and $2$ and $\omega/N = 0.65$ for mode$-3$, and a generator amplitude $a = 5\mathrm{~mm}$. The generator plate configuration for each mode is illustrated in the left hand column, with $n$ nodes for mode$-n$. The vertical cross sectional plots of the vertical velocity, presented in column $2$, possess the horizontal structure of the generator, increasingly intricate for the higher modes, with associated vertical sequences of maxima and minima. Columns $3$ and $4$ in figure~\ref{fig:fig3} present vertical and horizontal cross sectional plots of the radial velocity component. For every mode, the radial velocity structure possesses a left-right antisymetry in the vertical plane. The different nodes of radial velocity, which correspond to anti-nodes of vertical velocity, are also clearly visible in plots of the velocity in the horizontal plane, presented in column $4$; these images also show the form of the generator being reproduced by the underlying wave field. No orthoradial velocity $v_\theta$ was observed in the horizontal plane.
			\begin{figure}[!htbp]
				\begin{center}
					\begin{tabular}{>{\centering\arraybackslash}p{0.225\textwidth} >{\centering\arraybackslash}p{0.225\textwidth} >{\centering\arraybackslash}p{0.225\textwidth} >{\centering\arraybackslash}p{0.225\textwidth}}
						\hline
						$(1)$ Mode & $(2)$ $v_z$ (vertical) & $(3)$ $v_r$ (vertical) & $(4)$ $v_r$ (horizontal)  \\
						\hline \hline
						\multicolumn{4}{c}{\epsfig{file=fig3.eps}} \\
						\hline
					\end{tabular}
					\caption{Radial modes $1$, $2$, and $3$, as observed in PIV in the experiment. First column: generator configuration that sets the mode. Second column: vertical velocity in a vertical plane. Third and fourth columns: radial velocity in a vertical and in a horizontal plane. Shaded areas are outside of the confining cylinder. For the purpose of visualisation, negative values of $r$ are used in the vertical PIV plane, leading to antisymmetric radial velocities as predicted by equation~\eqref{eq:IW41}.}
				\label{fig:fig3}
				\end{center}
			\end{figure}

			In a previous study, Maurer \textit{et al}~\cite{maurer2017} experimentally measured the internal wave dispersion relation for freely propagating waves generated by an axisymmetric wave generator, which was consistent with theoretical predictions. In the modal configuration, however, the dispersion relation does not explicitly contain an angle of propagation, only a statement of the vertical wavelength as a function of the forcing frequency and horizontal wave number. The vertical wave number $m$ was measured for different frequencies $\omega/N$ for the three modes in our experiments. Figure~\ref{fig:fig4} compares the experimental values of $m$ with the theoretical one from equation~\eqref{eq:IW10}, when $f=0$. Measurements were performed by looking at the spatial vertical period of the vertical velocity on PIV images. It shows a good agreement for the three modes considered in the study, though there is a slight deviation at low frequencies, probably because of the error on $N$ which was about $10\%$ for mode$-1$ experiment and $4\%$ for mode$-2$ and mode$-3$ experiments.
			\begin{figure}[!htbp]
				\centering
				\epsfig{file=fig4.eps}
				\caption{Measured values of the vertical wave number (data points) for modes $1$, $2$, and $3$, compared to the theoretical expectations from equation~\eqref{eq:IW10}.}
				\label{fig:fig4}
			\end{figure}

			To quantitatively investigate how close the experiments reproduce the theoretical modal Bessel profile, figure~\ref{fig:fig5} presents radial profiles of $v_z$ and $v_r$, fitted to the expected radial dependency of the Bessel mode, for mode$-1$, mode$-2$, and mode$-3$ configurations. We see that $v_z(r) \propto J_0(l r)$ and $v_r(r) \propto J_1 (l r)$, with $l=19\mathrm{~m^{-1}}$, $35\mathrm{~m^{-1}}$, or $51\mathrm{~m^{-1}}$, as expected; these horizontal structures are preserved through the vertical propagation of the wave field. Small deformations sometimes appear close to the boundaries at $r=20\mathrm{~cm}$, due to boundary layer effects. The perturbation observed symetrically around $12\mathrm{~cm}< |r| < 16\mathrm{~cm}$ is actually caused by laser reflections in the cylinder, producing locally poor PIV visualisation.
			\begin{figure}[!htbp]
				\centering
				\epsfig{file=fig5.eps}
				\caption{From top to bottom: examples of experimental velocity profiles (left) $v_z$ and (right) $v_r$ for mode$-1$, mode$-2$, and mode$-3$, taken at a given time and altitude, fitted by appropriate Bessel functions: $J_0(lr)$ for $v_z$ and $J_1(lr)$ for $v_r$, with $l=19\mathrm{~m^{-1}}$, $l=35\mathrm{~m^{-1}}$, and $l=51\mathrm{~m^{-1}}$ respectively.}
				\label{fig:fig5}
			\end{figure}

		\subsection{Generator Efficiency}

		In order to investigate the resonance phenomena that is the topic of the following section, it is essential to reliably measure the amplitude of the internal wave field. Measuring the amplitude of internal waves in closed domains is a delicate task, however, more challenging than measuring their frequency or wavelength, due to unavoidable reflections. As such, we sought a robust measurement of wave amplitude and, further, to demonstrate it through studies of the efficiency of the wave generator, this being the ratio of the amplitude of the waves produced to the amplitude of the generator motion

		A few previous studies have made direct measurements of velocity amplitude, although these are typically done either at high frequencies or relatively high amplitudes. Mathur \& Peacock~\cite{mathur2010} studied transmission and reflection of internal wave beams across a transmission region and took a Fourier transform of the reflected and transmitted wave fields along appropriately chosen transects, Maurer~\cite{maurerPhD} measured wave amplitudes by looking at the maximum of the velocity over a given spatial area, and Supekar~\cite{supekar2018} utilized the distribution of maxima of amplitudes for a velocity field in a widespread two dimensional beam. In performing our experiments, it was necessary to more rigorously define our amplitude measurement methodology based on understanding of the group velocity of the wave fields we were studying.

	The procedure to determine the wave amplitude was the following. In a first step, experimental amplitudes at a given time $t_m$ were determined by fitting a Bessel function to the instantaneous horizontal profile at a given depth $z_{m}$ of the vertical velocity, as illustrated in figure~\ref{fig:fig5}. The depth $z_{m}$ chosen for this profile was selected to be $15\mathrm{~cm}$ below the generator, as the wave field was properly developed at this depth. Since the stratification, the forcing frequency and the radial wavelength are imposed, the only free parameter for the fit is the amplitude of the Bessel function. Note that we used the vertical velocity field for this fitting, since it has larger amplitudes than the radial velocity profile (which is characterized by a node at $r=0$) and so was more amenable to fitting.

			Measurements were repeated for all images over a time interval $t_m\in [t_i;~t_f]$, with $t_i$ being the time when the wave is expected to first cross the horizontal cross-section at $z=z_{m}$. The time $t_f$ is the time when the reflected wave is predicted to return from the bottom of the tank and reach $z=z_{m}$, resulting in a disturbance of the wave field. Both $t_i$ and $t_f$ were estimated using the group velocity of the wave field established in equation~\eqref{eq:IW14b}. This series of measurements provided a time-series of local wave amplitudes at $z=z_{m}$. An example of such a time series is shown in figure~\ref{fig:fig6}. One would expect this time signal to be sinusoidal. As can be seen in this example, the growth of the wave amplitude can still be slightly observed in the first periods, and the disturbance due to the returning wave is also observed for positive times (after $t=t_{f}$). This illustrates the difficulty of wave amplitude measurement in a finite size tank.

			In a second step, in order to best estimate the wave amplitude of the steady state before the reflected wave returned (there is some uncertainty on the exact return time), we computed the RMS value of the time signal over three periods close to $t_f$ half-covering each other, the middle one being just before theoretically seeing the reflected wave, the previous period covering the first half of this one, and the following period covering the second half of it (these measurement windows are illustrated by 3 rectangles in figure~\ref{fig:fig6}). The experimental global amplitude was determined as the mean value of the 3 RMS values obtained (multiplied by $\sqrt{2}$), and the standard deviation of these 3 measurements gives an estimate of the associated error. We checked that the method was sound by repeating some test measurements for other horizontal planes and obtaining consistent results.
			\begin{figure}[!htbp]
				\centering
				\epsfig{file=fig6.eps}
				\caption{Example of time series of fitted instantaneous Bessel function amplitudes of the vertical velocity, measured at $z=z_m=-15\mathrm{~cm}$ for a mode$-1$ wave. After identifying $t_f$ (solid vertical line), three periods half-covering each other (rectangles) are used to extract the global wave amplitude \textit{via} RMS estimates.}
				\label{fig:fig6}
			\end{figure}

			The results of our efficiency experiments are presented in figure~\ref{fig:fig7} for two different generator amplitudes. We plot the velocity amplitude normalised by the generator velocity amplitude $a\omega$. From equation~\eqref{eq:IW26}, without dissipation effects, one expects this ratio to be 1 (straight line in figure~\ref{fig:fig7}). This proves correct in the high frequency range ($0.5<\omega/N < 0.9$), except close to the buoyancy frequency as discussed below. In contrast, at low frequency, the efficiency decreases. This decrease can be interpreted by viscous effects. Indeed, when one includes viscous dissipation in the theoretical development, the expression of the stream function is given by equation~\eqref{eq:IW40}. The curve corresponding to the vertical velocity extracted from this equation (at a depth of $-15\mathrm{~cm}$ since equation~\eqref{eq:IW40} depends on $z$) is plotted in figure~\ref{fig:fig7}, showing a fair agreement with the experimental data points for the two forcing amplitudes $a=2.5 \mathrm{~mm}$ and $a=5 \mathrm{~mm}$. At very low frequencies (below $\omega/N = 0.05$), the amplitude is so low that measurements become impossible. Finally, for $\omega/N = 0.9$ to $1$, we notice a decrease in amplitude that is expected, as shown by the theoretical curve, since the waves are evanescent for $\omega/N > 1$. However, this decrease comes sooner than expected.

			 To conclude, the generator efficiency was investigated and shows a similar behaviour as the theoretical prediction in all frequency ranges, providing one takes viscous effects into account. In addition, we identify a range of frequencies, from $\omega/N=0.5$ to $\omega/N=0.9$, where there is a very strong agreement with the non viscous theory, making this range suitable for axisymmetric modes experiment and for resonant enhancement.
			\begin{figure}[!htbp]
				\centering
				\epsfig{file=fig7.eps}
				\caption{Generator efficiency measured at $z=-15\mathrm{~cm}$, for two experiments with $a=5\mathrm{~mm}$ and $a=2.5\mathrm{~mm}$. Results are compared to the theoretical predictions in the inviscid case and in the weakly viscous case (viscous damping curve, computed for $N=0.9\mathrm{~rad\cdot s^{-1}}$).}
				\label{fig:fig7}
			\end{figure}

		\subsection{Resonance}

		Having established the response of the stratification to the wave generator forcing, we then conducted experiments to detect resonance for a mode$-1$ excitation, due to the multiple reflections of the wave field at the top and bottom boundaries of the tank. These experiments consisted of measuring the amplitude of the wave after a time long enough to ensure the establishment of the steady state resonant wave field. In order to allow a minimum of about $10$ back and forth crossings, we chose this time to be $280\mathrm{~s}$, based of the minimum value of the group velocity of the waves. We thus looked for the maximum of vertical velocity at $r=0$ in a time period between $280$ to $300\mathrm{~s}$ (end of experiment duration) after the generator forcing was initiated. Using the vertical velocity at $r=0$ is optimal, as it is the highest velocity we can measure in the whole tank, and is straightforward since it corresponds to the amplitude of the velocity field.

		Our experimental results are presented in figure~\ref{fig:fig8}, showing the measured velocity amplitude, normalised by the generator velocity amplitude $a\omega$. We performed two sets of experiments : one with $a=2.5\mathrm{~mm}$ and $N\simeq 0.90 \mathrm{~rad \cdot s^{-1}}$ (blue circles) and another one with $a = 5\mathrm{~mm}$ and $N\simeq 0.88 \mathrm{~rad \cdot s^{-1}}$ (red squares). The first set of experiments was mainly aimed at identifying the resonant peaks; the second set was more evenly spread over all frequencies (a hundred values of $\omega/N$ from $0.625$ to $1$ at a regular interval). In the latter case, however, because of the larger generator amplitude, all experiments where the frequency was too close to the resonance led to strong non-linear effects, making the measurement of an amplitude impossible. For this reason, the corresponding data points are not shown. The theoretical curve for the maximal amplitude of vertical velocity normalised by the generator, computed from equation~\eqref{eq:IW35}, is also plotted in figure~\ref{fig:fig8} as a solid line.

		With the generator configured at low forcing amplitude ($a=2.5\mathrm{~mm}$), the peaks corresponding to the first resonant frequencies were observed as predicted by the theory (see table~\ref{tab:resonantomegas}). The measured resonance peaks are not exactly centered on the predicted resonant frequencies, but this is not inconsistent with the characteristic $4\%$ error on $N$. We see that in the vicinity of resonant frequencies the wave field reaches twice the amplitude of the generator, and even more for the highest frequencies. For non-resonant frequencies, however, the wave interaction is destructive and the measured amplitude is half the amplitude of the generator.
			\begin{figure}[!htbp]
				\centering
				\epsfig{file=fig8.eps}
				\caption{Amplitude measurements of the vertical velocity in the resonant cavity normalised by the generator velocity amplitude. Yellow line: theoretical amplitude for an infinite sum of waves as a function of the frequency $\omega/N$. The dots are from three different sets of measurements run for different buoyancies or amplitudes. Light gray regions show interval of frequencies in which non-linear effects are clearly seen in the experiment for $a=5\mathrm{~mm}$.}
				\label{fig:fig8}
			\end{figure}

			In the vicinity of a resonant excitation frequency, we observed that wave field amplitude kept strengthening until it triggered substantial non-linear effects. To illustrate this, figure~\ref{fig:fig9}  presents the temporal evolution of a horizontal profile of the vertical velocity component for $\omega/N=0.73$ (figure~\ref{fig:fig9}(a), non-resonant), and $\omega/N = 0.77$ (figure~\ref{fig:fig9}(b), resonant). In the non-resonant case, each velocity profile has the shape of a Bessel profile, which is conserved during the whole experiment. No non-linear deformation of the wave field can be observed. The amplitude shows a beating behaviour, because the reflected wave fields are not opposite in phase, due to the non-resonance condition. In the resonant case, such oscillations do not exist as all reflections are in phase. These reflections, however, lead to an increasing amplitude that quickly triggers non-linear effects, after $80$ seconds in the example in figure~\ref{fig:fig9}(b). The Bessel axisymmetric shape of the profile starts to disappear from the center of the tank due to emerging non-linear features, as the amplitude is maximum at $r=0$. The non-linearities then propagate radially towards the boundaries of the cylindrical tank, and the velocity field does not have a modal shape anymore (after $250$ seconds in figure~\ref{fig:fig9}(b)).

			By performing a similar analysis for all frequencies in the large amplitude case ($a=5\mathrm{~mm}$), we identified four frequency ranges in which all experiments led to non-linear effects. These ranges are marked with grey zones in figure~\ref{fig:fig8}. These intervals show a good agreement with the predicted resonance peaks (table~\ref{tab:resonantomegas}) and with the increasing amplitude observed for the low amplitude measurements ($a = 2.5\mathrm{~mm}$).
			\begin{figure}[!htbp]
				\centering
				\epsfig{file=fig9.eps}
				\caption{Temporal evolution of a horizontal profile of vertical velocity located at the center of the tank, for (a) $\omega/N = 0.73$ and (b) $\omega/N = 0.77$. These profiles are measured at mid-depth in the tank for a mode$-1$ excitation, with $a=5\mathrm{~mm}$.}
				\label{fig:fig9}
			\end{figure}

	\section{Conclusions and Discussion}

		We have presented the results of a laboratory experimental study of axisymmetric internal wave mode generation, incorporating both  radial and vertical confinement. To  support the experiments, we developed the theoretical framework of radial modes propagating vertically in uniform stratifications, accounting for the impact of weak viscous damping. The effect of rotation was not explored in our experiments, but the governing equations predict qualitatively similar behaviour as in the non-rotating case, the impact of rotation being foremost to influence the vertical wavenumber of the wave field for a given forcing frequency and buoyancy frequency. The experimental wave fields were produced using a novel configuration of internal wave generator technology that has previously been primarily used to excite nominally planar wave fields; in our experiments the arrangement directly excited the Bessel functions that are the natural basis of cylindrical modes.

	For the basic structure of the wave fields, there was very good qualitative and quantitative agreement between experiments and theory. Modes $1$ through $3$ were excited, leading to vertical and radial velocity profiles consistent with associated Bessel function forcing, and confirming the expected dispersion relation. As an additional component of these studies, we determined the efficiency of modal excitation by carefully studying the fluid system response to the generator forcing, fitting the PIV data to Bessel functions. A range of frequencies, from $\omega/N = 0.5$ to $0.9$, was identified as being particularly suitable for studying axisymmetric modes as in this frequency range the wave field is attenuated very little in the tank and has an almost full response to the forcing amplitude of the generator.

	Having established the ability to excite vertical modes, the role of vertical confinement was then investigated. Such confinement has the potential to generate a resonance effect when reflected modes constructively interfere with each other. The resonance conditions for our system were determined and a series of experiments with different forcing amplitudes were performed. The experimental results of wave field amplification aligned well with resonance predictions. Within the bounds of resonant peaks, the wave field was seen to amplify sufficiently to trigger nonlinear effects that then eroded the linear wave field structure outwards from the centerline of the experimental domain, ultimately leading to a fully non-linear wave field throughout the experimental domain.

	While there have been a number of nominally two-dimensional experimental studies comparing plane wave or mode behaviour with theoretical models, considering both their spatiotemporal form and transition to nonlinear phenomena, there have been few such studies for axisymmetric geometries, which have typically been limited to studying the wave field excited by an oscillating sphere. Axisymmetric wave fields are arguably more relevant as fundamental configurations for studying scenarios such as the excitation of atmospheric internal wave fields by storm cells~\cite{alexander1995} and the excitation of near-inertial wave fields in the ocean by surface storms~\cite{alford2003}. The experimental apparatus and consequent studies presented here demonstrate a new ability to excite axisymmetric wave fields and pure radial modes, opening the path to investigation of linear (e.g. internal wave transmission) and nonlinear (e.g. TRI) internal wave phenomena in axisymmetric geometries. For example, a recent study by Duran-Matute \textit{et al}~\cite{duranmatute2013} has used focusing by an oscillating torus to study the onset of instabilities; the vertical mode geometry we have developed and demonstrated here provides an arguably even more canonical configuration in which to study such non-linear phenomena, since any axisymmetric wave field can be expressed in terms of Bessel functions.

\medskip
\textbf{Acknowledgements:}

This work has been partially supported by by the ANR through grant ANR-17-CE30-0003 (DisET) and by ONR Physical Oceanography Grant N000141612450.

redpajama_set_name: RedPajamaArXiv


Congratulations to our Year 3 & 4 team who participated in the heats of the Dudley Maths Competition today.
The team did fantastically well, winning their heat by 9 points, beating schools including The Glynne, Caslon, St Joseph's and Greenfield.
They are through to the finals on 21st June 2017.


Three D News™® was hatched at about 3 am one sleepless night. My evening ritual has been to watch a bit of news before drifting off to sleep. That evening like a ton of bricks, I came to realize, what ever brand of news I was watching was selling their version of the truth and reality through a news editor. Not a unbiased accounting of the events and current news. I thought how two dimensional this form of media had become. Thus, it was not interesting, nor did I have faith in the information I was receiving. Now overlay this with the fact that I had just been in Las Vegas for the HUGE tech conference, where everyone is pushing 3 D technology screens.
I woke up in a sweat, proceeded to my GoDaddy account and registered Three D New.
The Vision is to have a site where you can get all the information you like about any news worthy event from a multitude of sources. There are usually differing opinions about how facts and events are interpreted. Now with a key stroke you can have a better picture of how the day, week, and year is unfolded. Additionally, we are going to be the first News Channel that will have 3 D capability. Computer and Smart phones are pushing hard on this technology, and we are going to be on the forefront of this explosive and exciting technology.
Three D News: A site that will actually have 3D content and gives the visitor enough information so they are not left in a 2 dimensional understanding of world and local events.
I hope you are as excited about this site as I am. After explaining the concept to a dozen top executives, tech titans, and social media gurus, they all gushed that the site had star power. Every person I asked to be a part of the site, from development, to our unique "Mega Blog", agreed on the spot!
We are always looking for talented news editors and contributors to our site.
Mega Blogger: A person that wants to blog and have a following on 3 D News.
For the right individual we are prepared to give a contributor a "Top" spot on the website.
We are always looking for on the ground content. News, life, love, jobs, in your opinion. Send us thoughts and have them viewed and loved by thousands…really millions….even bilions.
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text:
One of Latin America's oldest newspapers boosts color with Goss Community SSC press
June 17th, 2009 - Newspaper group Grupo Editorial El Siglo-La Estrella, based in Panama, recently went on production with a new Goss Community SSC press. The group publishes Latin America's second oldest newspaper, La Estrella, and national daily El Siglo.
The investment in the 28-unit Goss Community SSC press has increased both page and color capacity at the Grupo Editorial El Siglo-La Estrella facility in Panama City, enabling both newspapers to be printed in 100 percent color.
Juan Luis Correa, general manager of La Estrella and El Siglo, comments, "The investment in the Goss Community press came about as part of a project to redesign El Siglo and La Estrella. Not only have we gained increased color and enhanced print quality with the new press, but with the high speeds and reduced makereadies, we are also benefiting from many production improvements. We are very happy with the results so far."
The 560 mm cut-off press is configured as seven four-high towers with two SSC folders and produces the 64-page La Estrella broadsheet and the 56-page tabloid El Siglo, all in full color. The press operates at a maximum speed of 35,000 iph.
"With continuous technical upgrades the Community SSC press continues to be an extremely popular press across Latin America," comments Fernando Guerrero, sales manager for Goss International. "It's the best investment choice for publishers like Grupo Editorial El Siglo-La Estrella who are looking for premium print quality, high productivity and value."
Founded in 1981 El Siglo has a daily circulation of up to 40,000 copies. Sister publication La Estrella was founded in 1853 and has a circulation of 15,000 copies.
'Goss', the Goss logo, 'Goss International', 'Community' and 'SSC' are trademarks or registered trademarks of Goss International Corporation.

redpajama_set_name: RedPajamaCommonCrawl


text:
/*
 * SortTool.h
 *
 *  Created on: Apr 4, 2014
 *      Author: alex
 */

#ifndef SF1R_LASER_CLUSTERINGSORTTOOL_H_
#define SF1R_LASER_CLUSTERINGSORTTOOL_H_

#include <queue>
#include <string>
#include <boost/thread/thread.hpp>
#include <boost/thread/mutex.hpp>
#include <am/sequence_file/ssfr.h>
#include "laser-manager/clusteringmanager/type/Document.h"

#include <glog/logging.h>
namespace sf1r
{
namespace laser
{
namespace clustering
{

//template <class K, class V>
class ClusteringSortTool
{
private:
    std::queue<std::string> paths;
    int threadNum;
    boost::mutex io_mutex;
public:
    void run()
    {
        std::string path;
        while(getNext(path))
        {
            izenelib::am::ssf::Sorter<uint32_t, hash_t>::Sort(path);
        }
    }
    void start()
    {
        boost::function0<void> f = boost::bind(&ClusteringSortTool::run, this);
        std::vector<boost::thread*> thread_array;
        for(int i = 0; i < threadNum; i++)
        {
            boost::thread* bt = new boost::thread(f);
            thread_array.push_back(bt);
        }
        for(std::vector<boost::thread*>::iterator iter = thread_array.begin();
                iter != thread_array.end(); iter++)
        {
            (*iter)->join();
            delete (*iter);
        }
    }

    bool getNext(std::string& path)
    {
        boost::mutex::scoped_lock lock(io_mutex);
        if(paths.empty())
            return false;
        else
        {
            path = paths.front();
            paths.pop();
            return true;
        }
    }
    ClusteringSortTool(int thread, std::queue<std::string> path)
    {
        threadNum = thread;
        paths = path;
    }
};
} /* namespace clustering */
}
}
#endif /* CLUSTERINGSORTTOOL_H_ */

redpajama_set_name: RedPajamaGithub


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Let's adjust stop-loss levels on ZSL and DZZ.
I think it makes sense to secure some gains now by tightening up stop-loss levels on two positions: ProShares UltraShort Silver Fund (ZSL) and PowerShares DB Gold Double Short ETN (DZZ).
CANCEL AND REPLACE your order to sell all your shares of ProShares UltraShort Silver Fund, symbol ZSL, at $50.85*, STOP. New price: $64.86, STOP; this order is good till cancelled.
CANCEL AND REPLACE your order to sell all your shares of PowerShares DB Gold Double Short ETN, symbol DZZ, at $4.37, STOP. New price: $5.06, STOP; this order is good till cancelled.
Older PostExtending the scope of base-metal bearishness.


FLOATING OTHERS #2 comprises a set of mostly-improvised duets recorded in 5-Track's living room in Echo Park, Los Angeles, CA, Earth, sometime in the very warm part of 2012.
FREE DANNY ROSE — channelled from the logo on a handbill.
HOT AIR — a breath-based improvisation.
PEAKS & TROUGHS — Josh supplied a generator.
MINIATURE (or at least sub-mean) — a short piece from Josh.
737 — a longer piece from Josh.
NEIL WASHES HIMSELF — cribbed from one of 5-Track's notebooks.


text:
Evanoff: Memphians speak of racism, outrage, morality after MLK50
Let's take a minute to look at the mail that came in recently.
After The Commercial Appeal covered the 50th anniversary of Martin Luther King Jr.'s assassination in Memphis, several readers commented and asked questions.
"You call Al Sharpton a showman… but you don't understand the depth of the outrage African-Americans feel about this racist country."
Both the Rev. Sharpton, a New York activist, and President Donald Trump were described as "populist showmen" in a column last week.
While the reader pointed out Americans need to hear the message of activists such as Sharpton, I doubt history will connect Sharpton or Trump to a famous cause like FDR's New Deal or LBJ's Great Society.
Years ago, MLK did stand out. He gave voice to oppressed Americans. He delivered solutions such as the movement that helped usher the Civil Rights Act of 1964 through a Congress led primarily by conservative white men.
Today, preachers no longer seem able to stand prominently above the crowd with a moral authority that speaks to the entire nation.
You can come to Memphis and speak of police brutality, segregated schools, entrenched poverty and the moral outrage bred by injustice. You can speak of all this, and you can speak of this all year long, but what do we do about it?
It seems to me well-meaning Americans of all colors understand there are problems. What are the solutions? We see little direction coming out of Boston, New York, San Francisco, Washington or other American intellectual centers. What we do see is Trump's stand on import tariffs.
If this stand works, import restrictions could lead to factory construction in the United States. This could begin to shrink the income inequality that helps fuel the deep discontent voiced by activists like Sharpton. But major hurdles confront the trade stand.
The White House agenda of tax cuts and trade restrictions has no defined strategy to direct popular support at investors and corporate executives to get them to spend their tax windfall on job creation in the United States.
That's why I call Trump him a showman. I don't think he'll complete the hard work necessary to change the country's economic footing.
"Like everyone else in the media, you did not touch the third rail, that of culture as a contributor to our economic downturn. You mentioned that 62,000 single women (in Memphis) receive government support but did not suggest that a culture change of acceptance of that situation as the norm was a factor."
John Adams, the second president of the United States, long ago said the U.S. Constitution was "made only for a moral and religious people."
Having turned welfare into a moral right. I'd say the leadership of America can't suddenly demand a new moral attitude among welfare recipients, although leaders can provide a bridge in the form of education, day care, mass transit and economic development.
One other point bears mentioning. Several months ago, the United States stationed three aircraft carrier battle groups in the Western Pacific.
If we do cut off welfare for the poor, let's also raise taxes on U.S. corporations that at once demand tax relief in America and also produce overseas. If you want to enjoy the privileges afforded under our law, and the safety of bringing your imports ashore under the protection of men and women serving in our armed forces, pay your full share.
American poverty
"It seems to be clear that the number in 'poverty' is misleading because the income numbers do not include subsidized benefits (housing, medical care, earned income tax credits, transportation, food stamps, etc)."
Poverty is not the same as being destitute, not under federal guidelines.
The federal poverty threshold counts actual money such as supplemental Social Security but does not count non-cash support such as rent subsidies, food stamps or earned income tax credits.
In 2012, The Commercial Appeal published "Poverty Inc.," looking at the industry in Memphis that had grown up around the 100,000 poorest households. One article in that 2012 series pointed out: "Across the nation, households with an annual income of less than $10,000 lived on average as if they had made $21,000, according to a consumption survey last year of 122,287 households in all income strata by the U.S. Bureau of Labor Statistics.
"Government aid including welfare, food stamps, and rent subsidies accounted for the bulk of the $11,000 difference in the BLS survey. Off the books cash, the survey noted, averaged $1,100 per year, while annual Social Security payments added $2,800 per family."
"It was not just this week that thinkers (of which we should all be) and activists called for social progress. This has been a demand for years on end.
"We often do speak eloquently but a better suited word would be passionately as this is how (we) are about this work. We most certainly are on a mission. A mission to improve our city across the board and to have effective, respectable leadership in local government."
Ted Evanoff, business columnist of The Commercial Appeal, can be reached at evanoff@commercialappeal.com and (901) 529-2292.


The Arc of Attrition is a 100-mile coastal race from Coverack to Porthtowan in Cornwall (UK). The cut-off time for this race is 36 hours, with partial cut-off times set for the fully stocked four checkpoints along the route.
The course is coastal trail with small sections of road and is not waymarked.
The event requires self-navigation and partial self-sufficiency so the organisers have established entry requirements and proven experience. Support crews are welcome.
A carry kit is mandatory and is subject to random checks by the organisers.
In most people's minds running, I use the word running loosely here, a one hundred mile ultramarathon is pretty stupid, in fact at the time I couldn't even comprehend what running one hundred miles would feel like, let alone if this was achievable or not!
However, being the idiot that I am, I wanted to make this even more painfully difficult, so throw into the mix doing this along the South West Costal Path, a trail which would deliver both challenging going underfoot and terrain undulating enough to ascend almost half of Mount Everest, some 4000 meters of elevation gain in total.
Starting to see the theme here, oh and this would be my first one hundred mile race event, in fact it would be the first time I have run over 60 miles since World's Toughest Mudder in November 2016. On top of this for the most of December and January I have been injured, an injury I picked up during World's Toughest Mudder.
This was not going to be an easy affair.
The Arc of Attrition is an annual hundred mile ultramarathon organised by the crazy folks at Mud Crew, which in 2016 saw 72% of competitors DNF (Did Not Finish), the race is located in Cornwall and starts in the small village of Coverack and finishes one hundred miles later in Porthtowan. If you complete the race in under 30 hours you get the coveted 'golden belt buckle' if not its either black or red, not sure what the difference is, but those are the colours. The overall cut off for the event is thirty-six hours, so starting at midday on the Friday you have until midnight on the Saturday to finish the race, with tight cut offs throughout.
For me this was a brutal event, I had definitely underestimated the challenge, that was up until twenty four hours before the event when I started to realise what I had actually signed up for. And specifically, how little training I had done, leading up to the race the longest run I did in 2017 was a 27.4 mile trail marathon. I was not physically ready for this, and as I tried to sleep on the Thursday before we started, my lack of preparation started to play on my mind, what a bloody idiot!
Bottom line up front is that I finished, but it hurt and it took a long time, twenty nine hours and twenty four minutes to be precise.
For this race I planned to run with Andy from @andyontherun, Andy is a keen ultra runner, who has a few hundred mile races under his belt, and also managed to run from John O'Groats to Lands End in 17 days. So, I felt like I was in a safe pair of hands. We started steady, and positioned ourselves mid pack, this wasn't ideal though as the Costal Path was pretty narrow and soon our pace was very much dictated by the slower runners ahead of us, slower but perhaps wiser.
Eventually there was an opportunity to push on, and so I did, in true fashion I pushed a bit too hard to the first check point (CP) arriving at the 24.5 mile point 5 hours and 14 minutes later, not a great pace but still too fast for this distance based on my 'readiness' for this race. I had also lost Andy during this stage, so when I was about to leave this CP I told my awesome support crew, Vicky, to let Andy know I had set of too fast and that I was going to reduce my speed but keep moving, and that I looked forward to Andy catching me up.
As it turns out a few minutes before I left CP1, Andy arrived, allowing us to leave together. Next major stop was CP2 in Penzance, I don't remember much about this 13.9 mile section apart from there was a lot of road, which was just boring and flat, but unavoidable. From here it was back onto the trail for another 16.5 miles to Land's End, arriving at Land's End would see us hit the 55 miles mark and over half way, whoop!.
During this section was where we lost the light and we entered the 12 hours of darkness. We were both moving well on this section but the pace had dropped on my part. As it got dark we started to see more and more head torches on the route ahead, suddenly we got a bit more competitive and around mile 45 we started hunting down people, at this stage we were around 42nd and 43rd. Whilst this was fun, it was stupid on my part, I was in no position to be hunting down places and should have stuck to my original targets, hard target being to finish, stretch being to finish in under 30 hours.
Upon arriving into Land's End I was *****ed, trying to stick with Andy and trying to overtake people had taken its toll on me and my body. Andy was all good, but I was a bit of a wreck, I had a few blisters on my feet and the top of my femur bone was aching. I could see Andy was keen to get cracking, but I needed more time in the aid station, so we decided to part company here, I wouldn't see Andy again until the finish. In CP3 I had my feet taped up, I put some fresh socks on, had a quick massage to sort the pain around my femur and refuelled.
The next section, Land's End to St Ives was reported to be the hardest and gnarliest part of the course, a section which covered 24 miles and took on average 8 hours to complete in 2016. Not only was it really difficult to navigate, but the going underfoot was tough, and you were also surrounded by old mine shafts, and obviously massive cliff drops to your left. On top of this you had just completed 55 miles of undulating costal path.
It didn't start to well either, with a massive navigational issue in the village of Sennen Cove where I took a wrong turn and ended up lost, I knew I needed to be down by the sea front so cut across a fern/gauze hill and ended up in someone's back garden, before getting back on course. Lucky no one was in, or awake, or else I might have had some explaining to do. This was a long, hard and challenging section, there was definitely a few times where I ended up 'navigationally challenged' most scary of which was when I suddenly became aware of the fact that I was jogging along the edge of the cliff, and had to climb back up, and over a fence, to get back onto the costal path, this was around 4am and after 16 hours of running – scary stuff.
Eventually my battered body made in into St Ives, which was great, apart from the fact that no one could find CP4, there were 2-3 racers walking around like something out of 'The Walking Dead' looking for CP4, eventually after 5 – 10 minutes I found the CP. In the race briefing we had been told that CP3 to CP4 was where most people DNF'ed last year, and that everyone who made it to CP4 finished, so it was a relief to get there, even if I did say to Vicky that I didn't want to carry on.
Eventually I left CP4, 22 miles to go and at this stage I had 7 hours and 28 minutes to cover 22 miles if I wanted to get the golden buckle, and another 6 on top of that to finish within the 36 hour cut off. At this point was when I had my biggest ask of Vicky, basically I needed her to follow me home, there were opportunities to see each other, and grab any additional nutrition / kit around every 3 – 4 miles, and I took advantage of this as much as possible, a key highlight was the cheesy chips at the 96 mile point, I only wish I could have eaten more of them.
Over the last 10 miles the conditions deteriorated and there were stronger winds, hail stones and rain, bloody brilliant. The final 4 miles from Portreath to the finish had 3-4 killer climbs, just what you needed, but soon enough I saw the pink bobble hat of Vicky who had driven to the finish and climbed up the last 1km section of the course. When I saw Vicky, I knew there was no more climbing to be done, therefore it was time to push, there was a guy ahead of me who overtook me at Portreath and I was keen to get that place back, surprisingly I felt pretty nibble and managed a decent enough pace to the finish. I made it to the finish in a time of 29 hours and 24 minutes, so inside the 30 hour cut off for the golden buckle, I finished 27th in total, which I think is a decent enough position all things being considered.
Out of the 107 which signed up I believe 46% DNF'ed the race, so not as crazy as last year's DNF rate, but considering most people prepared for this event, that is still a pretty high DNF rate.
•	You really need to prepare for an event like this, I mean REALLY! Not just the mileage but also as it was a self-navigation race, learning the route beforehand would have helped, and would have been safer.
•	Tailwind nutrition is good for endurance events, I had never tried Tailwind before but Andy spoke highly of this, so I decided to buy some and used it throughout the event, topped up with water and some solid food at the CP's.
•	The importance of a good support crew, Vicky was AMAZING throughout this race, not only getting us to and from the event, but being at all the CP's, and every other access point she could. Just seeing someone helped, let along the bags full of stuff, those cheesy chips! And the mushroom toasties from Costa… amazing!
•	Pacing yourself is important, especially on long distance races, I went off too fast, but the fact I went from 43rd to 27th means a lot of people ahead of me either went off too fast also or were injured. It felt like people were racing the darkness, trying to get as far in as possible before it got dark, crazy.
•	Bush people make rubbish company! Between mile 55 and mile 78 I was pretty much on my own, and being a bit sleep deprived I start to see people, the reality is these weren't people, just bushes, I still said hello though, but they never responded.
In summary Mud Crew put on an amazing event, the CP's were well manned and well stocked, I wouldn't have finished in under 30 hours, or maybe even at all, if it weren't for my own support crew, so thank you so much Vicky. Will I do another 100 mile race? Definitely. Will it be the Arc of Attrition…..? No chance. That was too hard ha ha!
One of the best ultras I've done!
The organisation of this event was top notch, and all of the volunteers on the course were so warm and welcoming. The aid stations - albeit the few that there were - were really well manned.
Although the aid stations were every 20 or so miles, it made them all the more exciting!
The route itself was beautiful. The terrain underfoot was super boggy and slippery, but that just added to the experience.
If you're looking for an easy-breezy, flat 100, or a PB, then this probably isn't your bag. But if you're up for an adventure, and to submit yourself fully to the race, then I'd wholly recommend it.
Awesome race. Awesome company. Awesome organisers. PHENOMENAL atmosphere.


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Introduction:An acutely painful hip in a child can be the presenting symptom in a number of conditions. One of the most important conditions of which is septic arthritis of the hip for which early diagnosis and treatment is essential. The focus of management in acute hip pain in a child is to rule out septic arthritis as the penalty for missing a diagnosis of septic arthritis of the hip in a child has serious consequences .The purpose of our study is to add to the available pool of data on hip pain, validate the predictive values published by preceding authors. We also hope that by presenting the breadth and scope of patients presenting with an acutely painful hip with normal radiographs, we can assist the physician in decision-making when confronted with this common diagnostic challenge.
Methods: Retrospective review of all the patients who were admitted to our tertiary referral pediatric hospital with complains of hip pain and pain referable to the hip between January 1997 and December 2003. A total of 207 patients 162 patients with normal x-ray were reviewed retrospectively with evaluation of history, physical examination, laboratory studies. Patients whose diagnoses were defined as transient synovitis were made by the attending physician based on result of a combination of some or all of the Laboratory tests.( presence of fever, full blood count, Erythrocyte Sedimentation Rate (ESR) and C-reactive protein (CRP) levels, negative blood culture, and effusion on ultrasound, and clinical picture of early resolution. Patients whose diagnoses were defined as septic arthritis or probable septic arthritis were made based on the findings of elevated ESR, CRP, positive blood culture or hip aspiration culture.
Results: The 162 patients included 42 females and 120 males, with an age range from 6 months to 14 years. Of our cohort of patients admitted for hip pain, 111 patients were diagnosed as transient synovitis. 56 patients who were diagnosed as transient synovitis underwent ultrasound examination of the affected hip. 89.3% (50/56) had an effusion with a mean joint space thickness of 6.6mm. 10.7% (6/56) of the patients who underwent ultrasound examination had no demonstrable effusion.


text:
@class ElementSelector;
@protocol GREYAction;

namespace chrome_test_util {

// Action to longpress on the element selected by `selector` in the Chrome's
// webview. If `triggers_context_menu` is true, this gesture is expected to
// cause the context menu to appear, and is not expected to trigger events
// in the webview. If `triggers_context_menu` is false, the converse is true.
// This action doesn't fail if the context menu isn't displayed; calling code
// should check for that separately with a matcher.
id<GREYAction> LongPressElementForContextMenu(ElementSelector* selector,
                                              bool triggers_context_menu);

// Action to scroll a web element described by the given `selector` to visible
// on the current web state.
id<GREYAction> ScrollElementToVisible(ElementSelector* selector);

// Action to turn the switch of a TableViewSwitchCell to the given `on` state.
id<GREYAction> TurnTableViewSwitchOn(BOOL on);

// Action to turn the switch of a SyncSwitchCell to the given `on` state.
id<GREYAction> TurnSyncSwitchOn(BOOL on);

// Action to tap a web element described by the given `selector` on the current
// web state.
id<GREYAction> TapWebElement(ElementSelector* selector);

// Action to tap a web element with id equal to `element_id` on the current web
// state.
id<GREYAction> TapWebElementWithId(const std::string& element_id);

// Action to tap a web element in iframe with the given `element_id` on the
// current web state. iframe is an immediate child of the main frame with the
// given index. The action fails if target iframe has a different origin from
// the main frame.
id<GREYAction> TapWebElementWithIdInFrame(const std::string& element_id,
                                          const int frame_index);

// Action to scroll to top of a UIScrollView.
// On iOS 13 the settings menu appears as a card that can be dismissed with a
// downward swipe, for this reason we need to swipe up programmatically to
// avoid dismissing the VC.
id<GREYAction> ScrollToTop();

// Action to tap an element at the given xOriginStartPercentage as a percentage
// of the total width and yOriginStartPercentage as a percentage of the total
// height. Percentages are between 0 and 1, where 1 is 100%.
id<GREYAction> TapAtPointPercentage(CGFloat xOriginStartPercentage,
                                    CGFloat yOriginStartPercentage);

// Action to swipe a TableViewCell enough to display the "Delete" button and
// not too much to have the cell being deleted right away.
id<GREYAction> SwipeToShowDeleteButton();

}  // namespace chrome_test_util

#endif  // IOS_CHROME_TEST_EARL_GREY_CHROME_ACTIONS_H_


text:
Home » National » Congress distances itself from Aiyar's remark on Paris attack
Congress distances itself from Aiyar's remark on Paris attack
Jan 10, 2015 407 Viewed	Gautam Comments Off on Congress distances itself from Aiyar's remark on Paris attack
NEW DELHI: Congress on Friday distanced itself from Mani Shankar Aiyar's remark calling Paris massacre a backlash against the war on terror, saying the party's stand was reflected in the unqualified condemnation issued by Sonia Gandhi immediately after the attack.
Aiyar's statement, seen as rationalizing the shocking killing of 10 journalists in Paris, triggered a public debate with BJP wading into the controversy by seeking a statement from the Congress chief.
An embarrassed Congress termed Aiyar's statement as his 'personal opinion' while rejecting BJP's charge.
Party spokesperson Shobha Oza said, "Sonia Gandhi had condemned the Paris terror attack in the strongest possible terms. And after her statement, comments made by others have no meaning. It would have been better if BJP leaders had read her statement."
"It will be better if they start reading newspapers", she said adding no one could raise a finger against Congress on the issue of terror.
The response came after BJP questioned Gandhi's "silence" on Aiyar's statement and asked the opposition party to stop "vote-bank" politics.
The political controversy erupted after Aiyar called the attack on the satirical magazine Charlie Hebdo as an "obvious backlash" to the "war on terror".
He had said thousands (of Muslims) have been deprived of their family members, mothers and sisters in the war on terror that started after the twin tower attacks on 9/11. He mentioned there are drone attacks and issues like the outrage in Palestine to which there is no redressal.
"It is a horrible thing that has happened, I am outraged. However, there is no war in which the enemy does not hit back and what we are seeing is that terror groups are hitting back in the war against terror that was unleashed after the 9/11 attacks," he had said.
While drawing the link between the "horrible" attack on the cartoon magazine and the larger unrest in the Muslim world, Aiyar said, "There are family members of those who have suffered in this war on terror, who will react with violence."
PM Modi represents development, AAP represents drama: BJP
3 die as gelatin sticks explode in Satara


text:
Some Investors Flourish Despite Economic Tumult
NELSON D. SCHWARTZ
Jan 1, 2011 at 12:01 AM Jan 2, 2011 at 5:17 AM
In 2010, unemployment lingered in America and some European economies tottered, but investing in gold, industrials and many technology stocks turned out well.
An economy stuck in neutral. Unemployment that refused to go down. And a near financial disaster in Europe.
Despite all the negatives — and a few surprises, like the terrifying "flash crash" of the stock market in May — 2010 proved in the end to be a pretty good year for investors, especially if you were lucky enough to own shares in highflying technology stocks, old-fashioned industrials or gold.
"In many cases, the conventional wisdom was wrong," said Byron R. Wien, a veteran market strategist at the Blackstone Group. "The market still managed to do well, and the rise in gold and other commodities was a big surprise."
The typical equity fund in the United States returned nearly 19 percent in 2010, while the Standard and Poor's 500-stock index rose 12.8 percent. That was below the gains of 2009, when the markets rebounded from the financial crisis and the S.&P. index soared 23 percent.
Few expected such robust results for 2010 when the year began, said Tobias M. Levkovich, chief United States equity strategist at Citigroup.
"People were worried about interest rates going up, double dips and the housing market falling," Mr. Levkovich said, just to name a few of the concerns. Those fears have not disappeared, "but a level of optimism has returned. We didn't go off the cliff."
So why did stocks do well this year when so much seemed to be going wrong?
One factor, analysts say, was the unexpected surge in corporate earnings throughout the year, helped largely by cost-cutting. Then the government pitched in: The Federal Reserve's decision in early November to pump $600 billion into the economy by buying Treasury assets, along with tax cuts passed by the lame-duck Congress in December, helped propel a year-end rally, lifting the benchmark S.&P. index by about 6.5 percent in December alone.
On Friday, the Dow Jones industrial average rose 7.8 points, to 11,577.51. That made for an 11 percent gain in 2010. The Standard & Poor's 500-stock index was less than a point lower, at 1,257.64. The Nasdaq lost 10.11 points, or 0.38 percent, to finish at 2,652.87.
While stocks performed well over all, a small group of listings played an outsize role. Within the S.&P. 500, Mr. Levkovich said, the top 50 performing stocks contributed about 60 percent of the jump in the index.
Technology was again a star, paced by Netflix, up 219 percent, making it the single best performer in the index. F5 Networks, which makes equipment to manage Internet traffic, was No. 2, rising about 146 percent.
Cummins, the engine maker, took third place with a 140 percent gain. Automakers also did well, with Ford rising about 68 percent even as General Motors returned to the stock market in a $23 billion initial public offering, the biggest in United States history.
But many individual investors missed the party, having taken their money out of stocks. They were scared off, it seems, because of the volatility that followed the brief 1,000-point drop on May 6, the so-called flash crash, as well as lingering concerns from the financial crisis of 2008, including a housing and unemployment hangover.
"Investors in general tend to have a reduced tolerance for risk," said Brian Reid, chief economist of the Investment Company Institute.
The institute estimates that investors withdrew $80 billion from domestic equity mutual funds in 2010, while they added more than $250 billion to bond funds. To be sure, investors still have roughly $4 trillion in domestic stock funds, but that flight from the market is reflected in other figures, like shrinking trading volume.
Total volume was down 16 percent from 2009, and was 24 percent below the levels of 2008, according to Howard Silverblatt, a senior index analyst with Standard and Poor's. That ate into the results of major banks and brokerage firms, like Morgan Stanley and Charles Schwab, which rely on trading commissions.
The government bond market was precarious as well. Typically, bond prices go up and yields drop when economic growth is anemic, reversing course when economic activity picks up and the threat of inflation reawakens.
Indeed, as it became clear the economy was sputtering in the spring and the European debt crisis worsened, investors began pouring money into bonds, eventually sending yields to all-time lows by early October. The yield on the two-year government bond, for example, fell below 0.4 percent in early October, a record low.
On Friday, the Treasury's benchmark 10-year note rose 20/32, to 94 13/32, and the yield fell to 3.29 percent from 3.36 percent late Thursday.
But with the announcement of the Federal Reserve's aggressive asset-purchase program and the extension of Bush-era tax cuts that were due to expire, bonds began to sell off in November and December even as stocks rallied, sending yields higher.
James Caron, head of global interest rate and currency strategy at Morgan Stanley, said 2010 was a year of reversals in the bond market. He added, "You had a 180-degree shift from gloom and doom to optimism."
For the year, the typical bond fund returned 5.6 percent, according to Morningstar.
Bonds may be a traditional refuge in turbulent markets, but it was gold, a haven for value since ancient times, that really shined. Like bonds, gold benefited from a flight to safety spurred by the European debt crisis. But it also raced higher on fears that budget deficits in Western countries, including the United States, are unsustainable and that lax monetary policies would weaken the value of paper currencies over time.
"People are disenchanted with paper currencies. They want to own something real, and over centuries gold has proven to be real," Mr. Wien said.
The returns were real too, with the typical gold mutual fund, including mining companies and a range of precious metals, moving higher by 40 percent. Gold itself rose from $1,096.95 at the start of the year to $1,420.78 on Friday. Crude oil, another closely watched commodity, rose from $79.86 a barrel to $91.38 a barrel on Friday, after rising 78 percent in 2009.
Underpinning the rally, most analysts said, were strong earnings, but in what is likely to be a worry for next year, the profits were bolstered by job cuts and other restructuring efforts, rather than revenue growth.
In the third quarter of the year, for example, earnings were 31 percent higher than last year, but revenue increased by just 8 percent. The disparity was even greater in the first quarter, as earnings jumped 58 percent but revenue rose only 11 percent.
With only so much room to cut costs, analysts say that kind of performance will be difficult to repeat, perhaps boding ill for stocks this year. Analysts expect profits to increase by 13.4 percent in 2011, far lower than the estimated 37.8 percent gain for 2010, according to Thomson Reuters.
To make matters worse, Wall Street is brimming with optimism, which in the looking-glass world of investing can actually be a signal to sell.
"The good news has been priced in, and the potential negatives have been ignored," said Jason Hsu, chief investment officer of Research Affiliates, a money manager in Newport Beach, Calif., that oversees $70 billion in assets. "The market is going to get more nervous at these valuations."


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China: digital currency tests begin in Shenzhen and Suzhou
By Stefania Stimolo - 9 Dec 2019
The People's Bank of China PBoC has announced that it is organising a new test for the long-awaited digital state currency, mainly in the cities of Shenzhen and Suzhou.
According to reports, PBoC appears to have involved seven state-owned companies in the test. Specifically, it is a collaboration with four commercial banks and three telecommunications giants.
Moreover, it seems that the pilot programme tested by China focuses mainly on sectors such as medical care, education, trade and transport.
The involvement of telecommunication giants in the project seems to be essentially dedicated to the development of SIM cards with integrated e-wallets or to the creation of new independent wallet apps.
The two cities of Shenzhen and Suzhou will, therefore, be the first to see the implementation of the new digital currency of the Chinese State in different ways.
While the small-scale pilot project in Shenzhen has already been tested at the end of 2019, it is stated that in 2020 there will be two phases for its implementation in order to make it widely promoted in the territory.
With regard to Suzhou, however, the report states that the new currency could be tested directly, especially after the news that in November a fintech company supported by PBoC was looking for blockchain and crypto experts precisely in Suzhou.
With this new implementation, commercial banks would be able to obtain the digital currency from the PBoC by depositing the RMB reserve first. Users and companies would then be able to register their e-wallets with these commercial banks so they could use the new digital currency.
So, after declaring to be working on the national digital currency since 2014, China is back on the scene with regard to DCEP (Digital Currency Electronic Payment), constantly publishing new statements about it.
Just last month, in fact, it was revealed by Jack Lee of HCM Capital, Foxconn's private equity branch, that the new Chinese DCEP could be launched on the market in early 2020.
This period in China could be defined as a race against time, perhaps to, on the one hand, counteract the Facebook Libra project and, on the other, to be the leader of the current global movement, which has recently seen European countries as its protagonists.
In fact, last week, even the European Central Bank (ECB) revealed its propensity to develop its own digital currency if euro cross-border payments do not become faster and cheaper.
Not only that, together with the announcement of the ECB, the governor of the French central bank Francois Villeroy de Galhau has also revealed that they will be launching a project for electronic payments with digital currency in early 2020.
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Stefania Stimolo
Graduated in Marketing and Communication, Stefania is an explorer of innovative opportunities. She started out as a Sales Assistant for e-commerce, and in 2016 she began to develop a passion for the digital world, initially in the Network Marketing sector, where she discovered and became passionate about the ideals behind Bitcoin and Blockchain technology, which lead her to work as a copywriter and translator for ICO projects and blogs, and organize introductory courses.