The structure of strongly stratified flow over hills: dividing-streamline concept

In stably stratified flow over a three-dimensional hill, we can define a dividing streamline that separates those streamlines that pass around the hill from those that pass over the hill. The height H s of this dividing streamline can be estimated by Sheppard's simple energy argument; fluid parcels originating far upstream of a hill at an elevation above H s have sufficient kinetic energy to rise over the top, whereas those below H s must pass around the sides. This prediction provides the basis for analysing an extensive range of laboratory observations and measurements of stably stratified flow over a variety of shapes and orientations of hills and with different upwind density and velocity profiles. For symmetric hills and small upwind shear, Sheppard's expression provides a good estimate for H s . For highly asymmetric flow and/or in the presence of strong upwind shear, the expression provides a lower limit for H s . As the hills become more nearly two-dimensional, these experiments become less well defined because steady-state conditions take progressively longer to be established. The results of new studies are presented here of the development of the unsteady flow upwind of two-dimensional hills in a finite-length towing tank. These measurements suggest that a very long tank would be required for steady-state conditions to be established upstream of long ridges with or without small gaps and cast doubt upon the validity of previous laboratory studies.