The Three-Dimensional Asymmetric Holmboe Instability

The study of the conditions under which a stratified shear flow becomes turbulent is important, as turbulence is the source of mixing and dissipation in the atmosphere and can significantly influence the momentum and temperature structure of the atmospheric circulation. This study investigates the asymmetric Holmboe instability, which is the instability of a parallel shear flow of a stably stratified atmosphere with two layers of homogeneous but different density, where the interface of the two layers is not in the middle of the shear region, but at some height above it. We calculate the evolution of small-amplitude, three-dimensional perturbations around this background flow for various values of the Richardson number and of the non-dimensional asymmetry height. Instability is found for all values of the Richardson number and the asymmetry height with the most unstable modes being counter-propagating waves in the plane of the flow with differing wave speeds. The eastward propagating mode is found to have a larger scale and faster growth in comparison to the westward propagating mode. Both the scale and the growth rate of the most unstable waves were found to decrease with the Richardson number, while an increase in asymmetry was found to increase the scale and the growth rate of the most unstable eastward wave.