Title: Steady stratified flow over ridges: the hydraulic regime

Abstract:

Stratified flow passing over an obstacle induces a variety of motions that are often of interest in oceanic and atmospheric contexts where winds, currents and tides encounter topography frequently encounter topography of various shape and scale. Depending on several factors, a steady low-level flow can split horizontally to go around the obstacle, it can be swept up and over the obstacle inducing a strong internal wave response in the lee, or it can by hydraulically controlled at the crest, giving rise to strong downslope flows and turbulence.

In this talk, we revisit the classical problem where a uniformly stratified flow of constant speed approaches a two-dimensional ridge. We seek steady solutions in the regime where blocking and long, upstream-propagating waves alter the flow approaching the ridge to first order. By appealing to laboratory and numerical experiments, we show that this regime is characterized by a streamline bifurcation above and just upstream of the obstacle crest and that this results in the formation of a stagnant isolating layer and a hydraulically supercritical accelerated downslope flow in the lee. A nonlinear analytical solution is then developed that describes these flows in detail given the total transport of the flow, the stratification, and the height of the ridge crest.

The accelerated downslope flow is unstable and produces turbulence in the lee by two distinct processes. As the fluid above the downslope flow is stagnant, there is a region of strong shear that induces spatially growing instabilities and causes flow pulsations as noted by Scinocca and Peltier in 1989. In addition, the supercritical flow separates from the ridge and undergoes an internal hydraulic jump. The intensity of the turbulence within the jump depends on subcritical boundary conditions further downstream.

Finally, we use the analytical solutions in the hydraulic regime to consider how the solutions change when, keeping all other parameters fixed, the flow rate is increased. In this regime, blocking and upstream influence can no longer occur and the response becomes wavelike, amenable to a linear theoretical approach.