The two-dimensional flow of a stratified fluid over an obstacle

Abstract

The two-dimensional stratified flow over an obstacle placed in a channel of finite height is examined to determine the extent to which Long's model provides an adequate description of real flows. A simple numerical method of solving Long's model for obstacles of arbitrary shape is used to calculate predicted streamline patterns which are compared with experimental observations of the flow over two bluff obstacles. If only a few lee-wave modes are excited there is qualitative agreement between theory and experiment, but, if the flow is subcritical with respect to several lee-wave modes, the effects of turbulence become dominant and the inviscid model is no longer useful. The theory predicts that the drag on an obstacle can increase with decreasing speed owing to the momentum transfer to lee-wave motion. Direct measurement of drag indicates that there are conditions under which the drag does increase with decreasing speed, but under these conditions the wake is dominated by turbulence and no lee waves can be detected.