  We determine experimentally the angle $\alpha$ of maximum wave amplitude in
the far-field wake behind a vertical surface-piercing cylinder translated at
constant velocity $U$ for Bond numbers $\mathrm{Bo}_D = D / \lambda_c$ ranging
between 0.1 and 4.2, where $D$ is the cylinder diameter and $\lambda_c$ the
capillary length. In all cases the wake angle is found to follow a Mach-like
law at large velocity, $\alpha \sim U^{-1}$, but with different prefactors
depending on the value of $\mathrm{Bo}_D$. For small $\mathrm{Bo}_D$ (large
capillary effects), the wake angle approximately follows the law $\alpha \simeq
c_{\rm g,min} / U$, where $c_{\rm g,min}$ is the minimum group velocity of
capillary-gravity waves. For larger $\mathrm{Bo}_D$ (weak capillary effects),
we recover a law $\alpha \sim \sqrt{gD}/U$ similar to that found for ship wakes
at large velocity [Rabaud and Moisy, Phys. Rev. Lett. {\bf 110}, 214503
(2013)]. Using the general property of dispersive waves that the characteristic
wavelength of the wavepacket emitted by a disturbance is of order of the
disturbance size, we propose a simple model that describes the transition
between these two Mach-like regimes as the Bond number is varied. We show that
the new capillary law $\alpha \simeq c_{\rm g,min} / U$ originates from the
presence of a capillary cusp angle (distinct from the usual gravity cusp
angle), along which the energy radiated by the disturbance accumulates for Bond
numbers of order of unity. This model, complemented by numerical simulations of
the surface elevation induced by a moving Gaussian pressure disturbance, is in
qualitative agreement with experimental measurements.

Fluid Dynamics