Institute for Mathematics and Its Applications
James McWilliams, UCLA
The Lagrangian transport and mixing of material are explored in a geographically idealized numerical model of mid-latitude wind-driven gyres. Equilibrium solutions at low (just beyond the primary Hopf bifurcation) and relatively high Reynolds number are analyzed and compared from the Lagrangian viewpoint. The character of the time variability in these solutions differs considerably, from a geographically confined limit cycle, in the former case, to geographically extensive, broad-band fluctuations with considerable power at interannual periods in the latter. It is shown that a substantial part of the intergyre transport is done by coherent patterns, which trap fluid and carry it across the time-mean streamlines, and that the domain may be qualitatively partitioned into several regions characterized by distinct mixing scenarios and statistical distribution functions (PDFs). Techniques applied include ensemble analysis of particle trajectories and particle PDFs, calculation of invariant manifolds attached to certain hyperbolic points, dispersion, finite-time Lyapunov exponents, correlation dimension, and velocity spectra and PDFs. Consideration is also given to devising a stochastic trajectory model that mimics the transport in transient gyre solutions.