Leaving Flatland: 3-D Aspects of Lagrangian Coherent Structures

Methodologies arising from dynamical systems theory are widely used in oceanography to describe flow properties and quantify stirring processes. Of particular interest are special material curves that delineate transport pathways in transient mesoscale eddy fields. To date oceanographic applications have been almost entirely restricted to considerations of the near surface, with the tacit assumption of zero vertical velocity. Even in two dimensions, these material curves are tedious to calculate, and many scientists rely on surrogates such as finite time/space Lyapunov exponents to define Lagrangian Coherent Structures (LCS). Extending such dynamical systems concepts to include depth dependence in a realistic setting presents difficult computational and theoretical challenges. We discuss several of these here. Specifically, we use a range of models, from toy problems to regional data assimilating ocean models, to answer such questions as: Can 3D transport pathways in ocean general circulation models be adequately delineated by material surfaces derived from 2D curves at many levels and stitched together -- or are 3D trajectories, which rely on small and noisy vertical velocity estimates, necessary? How representative are near-surface LCS of LCS below 200 m? What is the shape of LCS around an individual eddy, especially near the bottom of the eddy?