### CKRT Jones

## Dynamical Systems Techniques in Ocean Flows

Questions about mixing and transport in fluid flows
raise some fundamental issues in dynamical systems. A
fluid particle follows a Lagrangian trajectory of the velocity
field which, in turn, is obtained from solving an appropriate partial
differential equation. To assess global reorganizations of the fluid
particles, structures such as invariant manifolds of hyperbolic
trajectories, invariant tori and other dynamic structures can be used
to great effect.

The challenges to dynamicist arise in the context of large-scale flows
such as occur in the ocean. Much activity in the ocean is mediated by
mesocale ($\sim$ 100 km) features such as eddies and jets. As these
structures move through ocean waters, fluid is exchanged between them
and the ambient water, as well as between their different internal parts.
Quantifying the extent of such transport and understanding the underlying
physical mechanisms responsible for it are important issues for
oceanographers.

All but the simplest model flows are given, however, as numerical
solutions of the relevant PDEs. This immediately puts the dynamicist
into new territory as techniques are needed that are adapted to velocity
fields given as numerical data. Moreover the flows are rarely periodic and
usually only known for finite periods of time.

In this contribution, the basic theory of transport due
to ``chaotic advection'' will be presented. Recent advances
will be described that extend the basic theory to the case of
``finite-time'' flows and applications of these techniques to
specific ocean scenarios will be described.

*
CKRT Jones *

May 18 1998