Observations of stratified flow over two-dimensional obstacles in fluid of finite depth

Abstract

This paper describes the results of an experimental study of stratified flow over two-dimensional obstacles in fluid of finite depth, with large Reynolds numbers and obstacle heights of about 1/10 channel depth or less. Both long and short obstacles have been used, and all aspects of the flow field are described in some detail. The observations are compared with relevant theoretical results, notably those from the linearized small obstacle height model. For supercritical flows (0 < K = ND /? U < 1) the linear theory gives a quite accurate description of the flow right up to very close to the critical speed ( K = 1), even though the linear model solution diverges as the critical flow speed is approached. For subcritical flows (where observations have been concentrated in the range where only the first lee wave mode is present (1 < K < 2)) the various properties of the lee wave field are reasonably well described by linear theory, but other aspects of the flow are not well described, particularly if the flow is just subcritical. Regardless of the smallness of the obstacle height, there is a finite parameter range (1 < K < K c ) where steady, columnar mode 1 structure is found upstream (“upstream influence”), in the same sense as described by Baines (1977) for larger obstacles, and this motion is not consistent with the small amplitude perturbation theory. This flow is apparently a permanent feature, with Kc tending to unity as the obstacle height h approaches zero. Flow fields over the obstacle show corresponding differences from linear theory, and similar behaviour occurs for the higher order modes. These phenomena must have a non-linear origin, and it is shown that they may be important in atmospheric flows. DOI: 10.1111/j.2153-3490.1979.tb00914.x