Abstract
AbstractHigh‐drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity‐wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed‐form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z1. Drag maxima correspond to constructive interference of the upward‐ and downward‐propagating waves in the region z<z1, while drag minima correspond to destructive interference. The reflection coefficient at the interface z=z1 increases as Ri decreases. The critical level, zc, plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where zc appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood. Copyright © 2005 Royal Meteorological Society.
Highlights
A substantial amount of the literature devoted to the study of orographic gravity waves in the atmosphere deals with the problem of resonant flows, high-drag states and downslope windstorms
High-drag states have been investigated in stratified flow over an axisymmetric mountain and a 2D ridge
Hydrostatic, analytical model, it was shown that, for a wind profile that is constant near the ground and decreases linearly with height, high-drag states exist even for infinitesimal dimensionless mountain heights
Summary
A substantial amount of the literature devoted to the study of orographic gravity waves in the atmosphere deals with the problem of resonant flows, high-drag states and downslope windstorms. Miranda and Valente (1997) addressed the case of flow with an environmental critical level over an axisymmetric mountain, showing that in this 3D configuration, the resonant drag enhancement and resonance shift are reduced relative to the 2D case, and the flow is closer to linear They found that the periodicity of the high-drag states as a function of the height of the critical level is of one half the hydrostatic vertical wavelength, in agreement with Clark and Peltier’s (1984) arguments. Wang and Lin (1999a, 1999b), following Lindzen and Tung (1976), studied the effects of wave ducting by shear layers for a wide range of Richardson numbers They suggested that the heights where the wind velocity has a discontinuity in its first derivative may be more important than the height of the critical level.
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