Upstream boundary-layer separation in stratified flow

Publisher Website
Google Scholar
Abstract
Stratified, inviscid channel flow over a thin barrier or into an abrupt contraction is considered on the hypotheses that the upstream dynamic pressure and density gradient are constant (Long's model) for those parametric régimes in which the hypotheses are tenable for finite-amplitude disturbances, namelyk< 2 for the barrier andk< 1 for the contraction, wherek=NH/πUis an inverse Froude number based on the Vaisälä frequencyN, the channel heightH, and the upstream velocityU. Reverse flow in the neighbourhood of the forward stagnation point, which implies the formation of an upstream separation bubble, is found for certain critical ranges ofk. The maximum barrier height for which the dominant lee-wave mode can exist without reversed flow either upstream or downstream of the barrier is 0·34H. The limiting case of a half space is considered briefly, and forward separation is found for κ =Nh/U> κs, where κs= 2·05 for a thin barrier and 1·8 for a semi-circular barrier. The corresponding values for reverse flow in the lee-wave field are κc= 1·73 and 1·3, respectively.