The Effect of Tilted Rotation on Shear Instabilities at Low Stratifications

Abstract

A linear stability analysis of the inviscid stratified Boussinesq equations is presented given a steady zonal flow with constant vertical shear in a tilted f plane. Full nonhydrostatic terms are included: 1) acceleration of vertical velocity and 2) Coriolis force terms arising from the meridional component of earth?s rotation vector. Calculations of growth rates, critical wavenumbers, and dominance regimes for baroclinic and symmetric instabilities are compared with results from the traditional nonhydrostatic equations, which include a strictly vertical rotation vector, as well as results from the hydrostatic equations. The authors find that for positive zonal z shear, tilted rotation enhances the dominance regime of symmetric instabilities at the expense of baroclinic instabilities and maintains symmetric instabilities at larger scales than previously indicated. Furthermore, in contrast to former studies, it is determined that hydrostatic growth rates for both instabilities are not maximal. Rather, growth rates peak in the fully nonhydrostatic equations for parameter regimes physically relevant and consistent with abyssal ocean stratifications and weak zonal z shears and oceanic measurements of the Labrador Sea and Southern Ocean. In addition, the authors find that zonal shear modifies the frequency range of subinertial inertio?gravity waves. Tilted rotation effects break the base flow shear reflection symmetry present in the traditional and hydrostatic models. Thus, only in the fully nonhydrostatic model does weak negative zonal z shear stabilize the flow and decrease the subinertial frequency range.