Three dimensional chaotic advection by mixed layer baroclinic instabilities

TL;DR

This study analyzes three-dimensional chaotic advection in mixed layer fronts caused by baroclinic instabilities, revealing complex stirring patterns, the influence of vertical shear, and the limitations of 2D approximations for mixing processes.

Contribution

It introduces a detailed analysis of 3D FTLEs in mixed layer fronts, deriving a scaling law and highlighting the importance of 3D structures in ocean mixing dynamics.

Findings

3D FTLEs exhibit complex, less defined structures than 2D FTLEs.

FTLE magnitudes are strongly influenced by vertical shear.

LCSs reveal filamentary structures not seen in Eulerian fields.

Abstract

Three dimensional (3D) Finite Time Lyapunov Exponents (FTLEs) are computed from numerical simulations of a freely evolving mixed layer (ML) front in a zonal channel undergoing baroclinic instability. The 3D FTLEs show a complex structure, with features that are less defined than the two-dimensional (2D) FTLEs, suggesting that stirring is not confined to the edges of vortices and along filaments and posing significant consequences on mixing. The magnitude of the FTLEs is observed to be strongly determined by the vertical shear. A scaling law relating the local FTLEs and the nonlocal density contrast used to initialize the ML front is derived assuming thermal wind balance. The scaling law only converges to the values found from the simulations within the pycnocline, while it displays differences within the ML, where the instabilities show a large ageostrophic component. The probability distribution functions of 2D and 3D FTLEs are found to be non Gaussian at all depths. In the ML, the FTLEs wavenumber spectra display -1 slopes, while in the pycnocline, the FTLEs wavenumber spectra display -2 slopes, corresponding to frontal dynamics. Close to the surface, the geodesic Lagrangian Coherent Structures (LCSs) reveal a complex stirring structure, with elliptic structures detaching from the frontal region. In the pycnocline, LCSs are able to detect filamentary structures that are not captured by the Eulerian fields.