  We develop a framework to study the role of variability in transport across a
streamline of a reference flow. Two complementary schemes are presented: a
graphical approach for individual cases, and an analytical approach for general
properties. The spatially nonlinear interaction of dynamic variability and the
reference flow results in flux variability. The characteristic time-scale of
the dynamic variability and the length-scale of the flux variability in a unit
of flight-time govern the spatio-temporal interaction that leads to transport.
The non-dimensional ratio of the two characteristic scales is shown to be a a
critical parameter. The pseudo-lobe sequence along the reference streamline
describes spatial coherency and temporal evolution of transport. For
finite-time transport from an initial time up to the present, the
characteristic length-scale of the flux variability regulates the width of the
pseudo-lobes. The phase speed of pseudo-lobe propagation averages the reference
flow and the flux variability. In contrast, for definite transport over a fixed
time interval and spatial segment, the characteristic time-scale of the dynamic
variability regulates the width of the pseudo-lobes. Generation of the
pseudo-lobe sequence appears to be synchronous with the dynamic variability,
although it propagates with the reference flow. In either case, the critical
characteristic ratio is found to be one, corresponding to a resonance of the
flux variability with the reference flow. Using a kinematic model, we
demonstrate the framework for two types of transport in a blocked flow of the
mid-latitude atmosphere: across the meandering jet axis and between the jet and
recirculating cell.

Fluid Dynamics;Dynamical Systems;Chaotic Dynamics;Atmospheric and Oceanic Physics