Chaotic advection by submesoscale processes in the ocean

Abstract

Oceanic motions at spatial scales of O(100) km and above, are quasi-two dimensional (2D) while dynamics at scales of O(1) km - also called submesoscale, are known to be quasi-three dimensional (3D). Stirring processes at the submesoscale therefore require a 3D treatment, which is considered in this thesis. A comparison of 3D and 2D Lagrangian flow diagnostics - the Finite Time Lyapunov Exponents (FTLEs) is made. 3D FTLEs are computed from numerical simulations of a freely evolving oceanic 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 2D FTLEs, suggesting that stirring is not confined to the edges of vortices and along filaments, thus posing significant consequences on mixing. The magnitude of 3D FTLEs is found to be strongly determined by the vertical shear. Maximising curves of FTLEs, also called Lagrangian Coherent Structures (LCSs), are found to successfully detect submesoscale filaments and vortices in locations where the Eulerian diagnostics are featureless. 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 derived scaling law converges to the values found from the simulations within the pycnocline, while it diverges from it in the ML where the instabilities show a large ageostrophic component. Also, probability distribution functions (PDFs) of 2D and 3D FTLEs are found to be non Gaussian at all depths of the channel. The non-Gaussianity of these PDFs suggests that parameterization schemes in existing numerical models should be improved. Finally, the same analysis as for the idealised simulations, is repeated with a realistic ocean simulation dataset in two case study regions of the Atlantic Ocean in order to understand the influence of the various ocean forcing sources on the FTLEs, and to also investigate the seasonal cycle of 2D and 3D FTLEs. It is found that FTLEs show a clear seasonal cycle with large values in winter and low values in summer. The seasonal cycle of 2D FTLEs is found to be modulated by the eddy kinetic energy (EKE) both at the surface and ocean interior. At the ocean surface, 3D FTLEs are modulated by the vertical shear of horizontal velocities, which shows minimal change between winter and summer, while in the ocean interior, 3D FTLEs yield the same seasonal behaviour as 2D FTLEs. However, the primary determinant of the seasonal cycle of FTLEs is found to be the deepening of the mixed layer in winter, which leads to the increase of available potential energy on which baroclinic instabilities draw.