Analytical Investigation on the 3D Non-Boussinesq Mountain Wave Drag for Wind Profiles With Vertical Variations
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摘要: 用WKB近似方法建立了表达三维地形重力波拖曳的解析Non-Boussinesq扰动模型，其中在大Richardson数条件下给出了（静力和非静力模型的）重力波拖曳及其地表扰动气压的二阶表达式．通过针对经典的理想化三维圆钟型山体的一个算例证明，当基流风速切变为线性时，重力波拖曳随着切变的增强而减弱；并且前向垂直切变（forward-shear，风速随高度增加）所对应的重力波拖曳比反向切变（backward-shear，风速随高度减小）所对应的重力波拖曳减弱得更快．这种现象与模型是否采用静力近似无关．
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关键词:
- 重力波拖曳 /
- Taylor-Goldstein方程 /
- 风切变 /
- WKB近似 /
- 圆钟型山体
Abstract: A new analytical model was developed to predict the gravity wave drag(GWD)induced by an isolated 3-dimensional mountain,over which a stratified,non-rotating Non-Boussinesq sheared flow is impinged.The model is confined to small amplitude motion and assumes the ambient velocity varying slowly with height.The modified Taylor-Goldstein equation with variable coefficients was solved with a Wentzel-Kramers-Brillouin(WKB)approximation,formally valid at high Richardson numbers. With this WKB solution,generic formulae,of second order accuracy,for the GWD and surface pressure perturbation(both for hydrostatic and non-hydrostatic flow)were presented,enabling a rigorous treatment on the effects by vertical variations in wind profiles.In an ideal test to the circular bell- shaped mountain,it was found,when the wind is linearly sheared,that the GWD decreases as the Richardson number decreases.However,the GWD for a forward sheared wind(wind increases with height)decreases always faster than that for the backward sheared wind(wind decreases with height).This difference is evident whether the model is hydrostatic or not.-
Key words:
- GWD /
- Taylor-Goldstein equation /
- wind shear /
- WKB approximation /
- circular bell-shaped mountain
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