Lagrangian transport structures for three-dimensional and time-dependent
fluid flows are of great interest in numerous applications, particularly for
geophysical or oceanic flows. In such flows, chaotic transport and mixing can
play important environmental and ecological roles, for examples in pollution
spills or plankton migration. In such flows, where simulations or observations
are typically available only over a short time, understanding the difference
between short-time and long-time transport structures is critical. In this
paper, we use a set of classical (i.e. Poincar\'e section, Lyapunov exponent)
and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent
structures) tools from dynamical systems theory that analyze chaotic transport
both qualitatively and quantitatively. With this set of tools we are able to
reveal, identify and highlight differences between short- and long-time
transport structures inside a flow composed of a primary horizontal
contra-rotating vortex chain, small lateral oscillations and a weak Ekman
pumping. The difference is mainly the existence of regular or extremely slowly
developing chaotic regions that are only present at short time.Comment: 9 pages, 9 figure
