Persistent presence of small vertical scale velocity features during three-dimensional equilibration of equatorial inertial instability

Abstract

Small vertical scale velocity features (SVSs) are ubiquitous in the upper equatorial ocean but their lifecycle and role in the large scale dynamics are only beginning to be understood. In this article, we study the development of SVSs generated through inertial instability of a prototypical equatorial zonal flow with a uniform meridional shear, U(y) = Λy. While previous studies employ a zonally symmetric setting, in which the flow is constrained to remain invariant in the streamwise direction throughout its evolution, here we use a fully three-dimensional framework. We choose a setting, in which the fastest growing linear modes are zonally symmetric and the initial perturbation is almost zonally symmetric, so that the flow remains nearly two-dimensional until the symmetric instability is fully neutralized. The secondary instabilities of the modified zonal mean flow favor zonally nonsymmetric modes, which leads to three-dimensionalization of the flow. It has been previously conjectured in the literature that the dominant secondary instability is an inflection point-type barotropic instability that favors disturbances with a large vertical scale and the necessary condition for which is the reversal of the meridional gradient of the background potential vorticity. We show that although the conditions necessary for barotropic instability indeed arise after the neutralization of the symmetric instability, the dominant secondary instabilities form a sequence of high vertical mode disturbances excited through zonally nonsymmetric inertial instability of the evolving zonal mean flow. The barotropic eddies, therefore, remain underdeveloped and do not play an important role in the dynamics. We cannot rule out the possible influence of the applied lateral hyperdiffusion (used to control near-grid point noise in the integrations) on the relative roles of barotropic and inertial instability. The competition between these two possible secondary instabilities needs further investigation with higher resolution experiments. We note, however, that when zonally asymmetric inertial instability is not possible (achieved here by shortening the zonal extent of the integration region while keeping the hyperdiffusion coefficient the same), barotropic instability fully develops and the flow is dominated by the barotropic mode.