Identifying unstable modes in stratified shear layers

Abstract

One interpretation of the mechanism of instability in stratified shear flows is based on the idea that two independently propagating waves may interact to cause mutual growth in one another. This theory is used in the present study to develop a diagnostic that can be used to identify different types of unstable modes. We focus on stratified shear layers that are susceptible to both the Kelvin–Helmholtz (KH) and Holmboe (H) modes of instability—though the formulation is more general. The diagnostic is found to be useful in differentiating between KH and H modes in the symmetric stratified shear layer (where the center of the shear layer and the density interface coincide). The asymmetric stratified shear layer is also examined since there is no clear distinction between KH- and H-type modes in this flow. The KH mechanism of growth is predicted to extend to stronger stratifications (i.e., larger bulk Richardson numbers) than in the symmetric case, in qualitative agreement with nonlinear numerical results. However, the transition is found to be a gradual one in which the KH mechanism gives way to the H as the bulk Richardson number is increased. In order to demonstrate the utility of the method, we apply it to instability observed in the Fraser River estuary.