On The Richardson Number Dependence of Nonlinear Critical-Layer Flow over Localized Topography

Abstract

Abstract The dynamics of stratified shear flow over localized topography in two spatial dimensions is investigated through analysis of a sequence of nonlinear numerical simulations. The existence of a critical level for all stationary waves is ensured by employing a hyperbolic tangent profile of horizontal wind such that the shear is localized at some elevation ẑc and the flow is asymptotic to a speed −U0 above and +U0 below this level. Previous studies of this problem have investigated the dependence of the quasi–steady-state solution upon the critical-level elevation ẑc and on the strength of the topographic forcing. In the present study these analyses are extended to include an investigation of the dependence of the solution on the third and final governing parameter, namely the minimum gradient Richardson number Rm. Contrary to previous implicit assumption, we find that the temporal evolution of the flow towards the high-drag state can be strongly influenced by the value of Rm, to a degree that depe...