Analytical Investigation on the 3D Non-Boussinesq Mountain Wave Drag for Wind Profiles With Vertical Variations

TANG Jin-yun; TANG Jie; WANG Yuan

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(3): 288-296

TANG Jin-yun, TANG Jie, WANG Yuan. Analytical Investigation on the 3D Non-Boussinesq Mountain Wave Drag for Wind Profiles With Vertical Variations[J]. Applied Mathematics and Mechanics, 2007, 28(3): 288-296.

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Analytical Investigation on the 3D Non-Boussinesq Mountain Wave Drag for Wind Profiles With Vertical Variations

The Key Laboratory of Mesoscale Severe Weather, Ministry of Education; Department of Atmospheric Sciences, Nanjing University, Nanjing 210093, P. R. China

Received Date: 2005-10-18
Rev Recd Date: 2006-10-31
Publish Date: 2007-03-15

Abstract

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.
- GWD,
- Taylor-Goldstein equation,
- wind shear,
- WKB approximation,
- circular bell-shaped mountain

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References(13)

References

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