Stratified flow over topography: the role of small-scale entrainment and mixing in flow establishment

Abstract

Stratified flow over topography is examined in the context of its establishment from rest. A key element of numerical and steady-state analytical solutions for large amplitude topographic flow is the splitting of streamlines, which then enclose a trapped wedge of mixed fluid above the rapidly moving deeper layer. Measurements have been acquired that illustrate the development of this wedge and the role played by small-scale instabilities and mixing formed initially by the acceleration of subcritical stratified flow over the obstacle crest. The volume of trapped fluid progressively increases with time, permitting the primary flow to descend beneath it over the lee face of the obstacle. Throughout the evolution of this flow, small-scale instability and consequent entrainment would seem to be a prime candidate for producing the weakly stratified wedge, thus allowing establishment of the downslope flow to take place. Velocity structure of instabilities within the entrainment zone is observed and the associated entrainment rate determined. The entrainment is sufficient to produce a slow downstream motion within the upper layer and a density step between the layers that decreases with downstream distance. The resulting internal hydraulic response is explained in terms of a theory that accommodates the spatially variable density difference across the sheared interface. The measurements described here were acquired in a coastal inlet subject to gradually changing tidal currents. It is proposed that the observed mechanism for flow establishment also has application to atmospheric flow over mountains.

Internal hydraulic flows on the continental shelf: High drag states over a small bank

“…From our measurements over Stonewall Bank we show that the energy lost by the mean flow is dissipated locally, presumably by the processes identified by Farmer and Armi [1999b]. Comparison with two-layer theory indicates that little energy remains for internal wave generation.…”

“…We attribute the enhanced mixing observed here (e --• 10 -6 m 2 s -3) to shear instabilities that form in the accelerating flow region preceding an internal hydraulic jump [Lawrence, 1993;Farmer and Armi, 1999b;Pawlak and Armi, 1998]. Although our velocity measurements are not sufficiently resolved to explicitly determine the Richardson number (/i•i -N2/(dU/dz)2; N 2 = -(t7/p)(dp/dz)), an estimate may be made by as- …”

On the onset of bora and the formation of rotors and jumps near a mountain gap

“…At this point, we should note that two fundamentally different mechanisms have been proposed in the literature in order to explain the formation of such a wedge of neutrally-stratified air (see, for example, references on this topic in Mayr et al (2007)). Measurements of flows over an oceanic sill suggest that this wedge is formed by turbulent mixing due to small-scale shear instabilities (Farmer and Armi, 1999); whereas numerical simulations of the same case support the wave-breaking explanation (Afanasyev and Peltier, 2001 Figure 12) support shear-induced mixing as the mechanism.…”

Large Amplitude Breaking Internal Waves: Their Origin and Dynamics

“…Initial effort was focused on large amplitude internal wave generation, leading to analysis of the strongly forced case of flow over a sill (Farmer & Armi 1999, Armi & Farmer, 2002 and the generation of a nonlinear wave train through steepening of an upstream subcritical response (Cummins, Vagle, Armi & Farmer, 2003).…”