On the Richardson number dependence of nonlinear critical-layer flow over localized topography

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 z̄c and the flow is asymptotic to a speed -U0 above and +U0 below this level. We find that the temporal evolution of the flow towards the high-drag state can be strongly influenced by the value of R̄m, to a degree that depends upon the strength of the topographic forcing. The sense of this parameter dependence is such that, as the value of R̄m is decreased (with R̄m > 0.25 always), the transition to the severe downslope windstorm state is progressively delayed and for moderate topographic forcing (characterized by an inverse Froude number of 0.5) may possibly be prevented. Furthermore, we find that when this dependence is taken into account, there appears no evidence that would support the occurrence of a "resonance shift' which has been suggested in several previous analyses of this problem. -from Authors