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

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.