What happens when an inertially unstable jet approaches a lateral boundary?

Much of our understanding of inertial instability in geophysical flows comes from atmospheric physics, and these studies have neglected the impact of lateral boundaries. To address this shortcoming, we performed a series of high-resolution 3D numerical simulations in Oceananigans in the context of the nonhydrostatic Boussinesq equations assuming a rigid-lid approximation. An inertially unstable baroclinic jet was investigated both far away and adjacent to a vertical boundary. The jet was chosen to be in thermal-wind balance and the buoyancy field was perturbed to instigate the instability.

We found that when the unstable jet is sufficiently close to the vertical boundary, the wavenumber of the fastest-growing unstable mode nearly doubled when compared to the jet far away from the boundary. We have not observed this shift to smaller scales in the context of a barotropic jet. The growth rates of the instability, measured by taking the l² norm of the velocity components, showed an initial linear growth phase in the first few days with no significant differences regarding the positioning of the jet. After this period, non-linear saturation stabilized the jet to inertial instability, and a secondary baroclinic instability developed. These findings suggest a previously unaccounted factor that can influence the bio-physicochemical properties of the ocean in proximity to coastal boundaries, contributing to the current understanding of the importance of submesoscale phenomena.