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The dynamics of upstream blocking and hydraulic control in continuously stratified flow past topography

  • Author(s): Jagannathan, Arjun
  • Advisor(s): Winters, Kraig B
  • Armi, Laurence
  • et al.
Abstract

Upstream flow blocking is a distinguishing feature of stratified flows incident on dynamically tall mountain ridges. Blocking occurs as a consequence of the upstream propagation of long internal wave modes that are excited at the obstacle and which permanently modify the oncoming flow. When the ridge is infinite, the fluid upstream and below a `blocking level' is brought to stagnation. The resulting across-crest asymmetry combined with volume transport constraints causes the overflowing layer to accelerate and develop into a hydraulically controlled flow. The processes leading to the establishment of upstream blocking and hydraulic control occur on a characteristic short time scale. In the interior of a long, but finite ridge, a hydraulically controlled overflow similarly develops on a short time scale, while over a longer time scale, low-level horizontal flow splitting leads to the establishment of an upstream layer-wise potential flow beneath the blocking level. We demonstrate through numerical experiments that for sufficiently long ridges, crest control and streamwise asymmetry are seen on both the short and long time scales. We then proceed to quantify the overflow using the framework of stratified hydraulics.

In a separate study, we investigate the dynamic stability of stratified flow configurations characteristic of blocked, topographically controlled downslope flows. The essential character of the base flow profiles considered is determined by the analytical solutions of Winters and Armi (2014). Their condition of optimal control necessitates a streamline bifurcation above the blocking location, which then naturally produces a stagnant isolating layer overlying an accelerating downslope flow. We show that the inclusion of the isolating layer is an essential component of the stability analysis. The spatial stability problem is also examined in order to estimate the downstream location where finite amplitude features might manifest in streamwise slowly-varying flows over topography.

Finally, to expose the dynamical connection between topographic control and wave excitation aloft, we consider flow over dynamically tall ridges under stratification conditions that feature a strong density jump above crest level. We show that the height of the bifurcating streamline depends sensitively on the location of the step. Further, the question of whether or not the density interface remains flat or plunges across the crest as part of the hydraulically controlled flow is found to be directly related to the requirement of maintaining a subcritical overflow upstream. We also demonstrate that the top of the density interface acts as a `virtual topography' for the flow aloft and fundamentally controls the amplitude of the wave response there.

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