The Semigeostrophic Weir: A Simple Model Of Flow over Mountain Barriers

Abstract

Conventional inviscid theories of flow over smooth orography assume that boundary streamlines do not separate and that, for steady solutions, the orographic surface is isentropic. Cullen et al. describe an element model based on the Lagrangian form of the semigeostrophic equations which does exhibit a type of separation, even though viscous or boundary layer effects are absent. Further examination of this class of solution is made here with a two-fluid model, giving particular emphasis to the implied orographic drag and energy dissipation. Some simple analytic solutions are included, which show the onset of this geostrophic separation process (usually described as the breakdown of semigeostrophic theory). It is suggested that a substantial proportion of the measured orographic drag force on mountain ranges such as the Alps may be associated with turbulent energy dissipation immediately downstream of the mountain.