Two-dimensional Ekman-Inertial Instability: A comparison with Inertial Instability

In the ocean, submesoscale flows tend to undergo several hydrodynamic instabilities. In particular, Inertial Instability (InI) and Ekman-Inertial Instability (EII) are known to develop in geostrophically balanced barotropic flows whose lateral shear is larger in magnitude and opposite in sign to the Coriolis parameter. Although these instabilities share some elements, their dynamical nature can lead to fundamental differences. However, the current analytical description of EII is one-dimensional, which makes it difficult to compare against InI in a more realistic scenario. To overcome this limitation, we conduct two-dimensional numerical simulations of both InI and EII in a submesoscale jet and explore the induced vertical flow, the growth rate, and the energetics of each instability. Furthermore, we investigate the sensitivity of our results to variations in the minimum Rossby number of the jet. We find that EII grows faster than InI and induces stronger vertical flow, especially near the surface. Both instabilities radiate inertial waves away from the current, and these waves predominantly propagate across the anticyclonic side of the jet. Finally, when the instabilities weaken, the fluid reaches a stable state that is remarkably similar in both cases. This study highlights the similarities and differences between InI and EII and provides further insight into the mechanism behind EII that makes it capable of outcompeting other submesoscale instabilities.