Stability of stratified downslope flows with an overlying stagnant isolating layer

Abstract

We investigate the dynamic stability of stratified flow configurations characteristic of hydraulically controlled downslope flow over topography. Extraction of the correct ‘base state’ for stability analysis from spatially and temporally evolving flows that exhibit instability is not easy since the observed flow in most cases has already been modified by nonlinear interactions between the instability modes and the mean flow. Analytical studies, however, can yield steady solutions under idealized conditions which can then be analysed for stability. Following the latter approach, we study flow profiles whose essential character is determined by recently obtained solutions of Winters & Armi (J. Fluid Mech., vol. 753, 2014, pp. 80–103) for topographically controlled stratified flows. Their condition of optimal control necessitates a streamline bifurcation which then naturally produces a stagnant isolating layer overlying an accelerating stratified jet in the lee of the topography. We show that the inclusion of the isolating layer is an essential component of the stability analysis and further clarify the nature and mechanism of the instability in light of the wave-interaction theory. The spatial stability problem is also briefly examined in order to estimate the downstream location where finite-amplitude features might be manifested in streamwise slowly varying flows over topography.