Stratified flow past a hill: application of the dividing streamline concept

When a stably stratified flow passes an obstacle, under certain conditions a part of the flow goes over the topography while the rest moves around it. The demarcation between the two types of flow is signified by the dividing streamline, and its height Hs from the ground is related to the Froude number Fr=U∞/(N∞ h) , where U∞, N∞ and h are the characteristic velocity and buoyancy frequency of the upstream flow and the topographic height respectively. A dividing streamline usually exists when Fr≤O(1), and its height is represented by the Sheppard?s formula which is based on energetics. A new analytical solution for Sheppard?s formula is presented and compared with iterative solutions based on numerical computations, and the simple Hs/h=(1-Fr) formula based on the restrictive assumption of homogeneity of flow. The new solution was found to yield excellent results. Several important dimensionless parameters determining the dividing streamline height are delineated. A field experiment was designed to observe the dividing streamline height, which capitalized on a suite of instrumentation used in the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program. Multiple releases of smoke were made over several days in the MATERHORN-Spring experiment, and the observed dividing streamline height was in good agreement with the theoretical prediction. No dividing streamline was present for Fr>1, and the observed flow separation and vortex shedding were all indicative of inertially dominant flow.