Three dimensional chaotic advection by mixed layer baroclinic instabilities

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. Finite Size Lyapunov Exponents (FSLEs) are used to investigate the dispersion regimes, showing a Richardson regime, followed by a diffusive regime for scales smaller than the deformation radius at all depths. 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 both filamentary and elliptic structures that are not captured by the Eulerian fields.