Analysis of numerical stability of algebraic oceanic turbulent mixing layer models

In this paper, we study the stability of oceanic turbulent mixing layers by the finite element method with respect to perturbations of the data. We prove that the equilibria states depend continuously on the data, and that they are asymptotically stable in time, when approximated by standard numerical schemes. We also perform some numerical tests for realistic initial conditions, that also show that the mixing-layer configurations are stable under perturbations of the data, in addition to confirm the theoretical expectations of our analysis.