Out of flatland: Three-dimensional aspects of lagrangian transport in geophysical fluids

Lagrangian analyses based on dynamical systems theory have revealed complex transport pathways and barriers in both the atmosphere and ocean, often referred to as Lagrangian coherent structures (LCS). Since computation of the precise manifolds that define LCS is labor intensive, they are often approximated using finite time Lyapunov exponents (FTLE). Little is known about the 3-D character of LCS, since to date most LCS studies of geophysical flows have been restricted to 2-D analyses on a few selected surfaces. Computing full 3-D FTLE estimates that include combined dispersive effects due to vertical velocities and vertical shear in horizontal velocities can be challenging. A primary concern is whether the use of uncertain diagnostic vertical or diabatic velocities from quasihydrostatic models adds value to FTLE computations. We investigate this issue using an analytic quadrupole model where the LCS positions are known, and the vertical velocities are analytically prescribed.We quantify the differences between full 3-D FTLE and the frequently used 2-D approximation (based on 2-D trajectories), and we suggest a scalar measure of the vertical shear of the horizontal velocities as a diagnostic for identifying cases when the 2-D approximation may fail.