Strongly stratified flow past three‐dimensional obstacles

Abstract An experimental study has been made of the shear flow of stratified fluid of characteristic buoyancy frequency 𝒩 with characteristic speed 𝒰 past a three‐dimensional obstacle of height 𝒽 when the Froude number, Fr = 𝒰𝒩 𝒽, is much smaller than one. It is already known that in the limit Fr →O the inviscid equations of motion may be expanded in powers of Fr 2 and that the lowest‐order solution is a flow confined to horizontal planes, passing around the obstacle rather than over it. This theory breaks down within a distance 𝒰/𝒩 from the level of the top of the obstacle. The experiments were carried out in a closed‐circuit stratified water channel with a hemisphere, a cone and a truncated cylinder for Fr between 0.03 and 0.3 at Reynolds numbers between 100 and 1000. The qualitative features have been determined by flow visualization with dye. The flows are found to be nearly in horizontal planes except near the tops of the obstacles. Also there are revealed two other prominent features which the theory cannot predict. In the lee of the obstacles at the level of the top, a cowhorn‐shaped eddy with horizontal axis is observed for high enough Fr ; it combines the characteristics of rotors and of horseshoe vortices. Below this level, there is a separated wake flow in each horizontal plane. Vortices are shed provided the Reynolds number is large enough and provided Fr is less than about 0.15. The shedding frequency is the same at all heights. Attention is drawn to atmospheric situations of which these features may be ingredients.