Low Froude number flow past three-dimensional obstacles. Part II: upwind flow reversal zone

The present paper contains a continuation of our study of the flow of a density-stratified fluid past three-dimensional obstacles for Froude number ~O(1). We have excluded the effects of friction, rotation, nonuniform ambient flow, and the complexity of realistic terrain. Herein we examine the zone of flow reversal on the windward side of the obstable, which is also a characteristic feature of the low-Froude number flow. We find that flow stagnation and a tendency for flow reversal upwind of a symmetric bell-shaped obstacle is well predicted by linear inviscid gravity-wave theory. This finding stands in contrast with "horseshoe-vortex' arguments often invoked in the literature. We also perform experiments on obstacles of varying aspect ratio, β (across-stream length/along-stream length). Here the utility of the linear theory is less clear: considering cases with Fr=0.33 and β→∞, we find that for β≤1 upstream-propagating columnar modes are essentially absent, however, for β increasing beyond unity, they appear with increasing strength. -from Authors