Analytical Investigation on the 3D Non-Boussinesq Mountain Wave Drag for Wind Profiles With Vertical Variations
-
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．
-
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
-
[1] Blumen W.A random model of momentum flux by mountain waves[J].Geofys Publ,1965,26(2):1-33. [2] Teixeira M A C,Miranda P M A,Valente M R,et al.An analytical model of mountain wave drag for wind profiles with shear and curvature[J].J Atmos Sci,2004,61(9):1040-1054. doi: 10.1175/1520-0469(2004)061<1040:AAMOMW>2.0.CO;2 [3] Queney P. The problem of air flow over mountains: a summary of theoretical studies[J].Bull Amer Meteor Soc,1948,29(4):16-26. [4] Scorer R S.Theory of waves in the lee of mountains[J].Quart J Roy Meteor Soc,1949,75(2):41-56. doi: 10.1002/qj.49707532308 [5] Smith R B.The influence of mountains on the atmosphere[J].Advances in Geophysics,1979,21(3):87-230. doi: 10.1016/S0065-2687(08)60262-9 [6] Smith R B.Linear theory of stratified hydrostatic flow past an isolated mountain[J].Tellus,1980,32(4):348-364. doi: 10.1111/j.2153-3490.1980.tb00962.x [7] Bretherton F P.Momentum transport by gravity waves[J].Quart J Roy Meteor Soc,1969,95(404):213-243. doi: 10.1002/qj.49709540402 [8] 布赖姆 E O.快速傅立叶变换[M].柳群 译.上海：上海科学技术出版社，1979，72-75. [9] Drazin P G.On the steady flow of a fluid of variable density past an obstacle[J].Tellus,1961,13(2):239-251. doi: 10.1111/j.2153-3490.1961.tb00081.x [10] Landau L D,Lifshitz E M.Fluid Mechanics, 2nd Edition[M].Oxford:Butterworth-Heinemann,Pergamon Press.1987,3-4,29. [11] Booker J,Bretherton F P.The critical layer for internal gravity waves in a shear flow[J].J Fluid Mech,1967,27(3):513-539. doi: 10.1017/S0022112067000515 [12] Miles J W.On the stability of heterogeneous shear flows[J].J Fluid Mech,1961,10(4):496-509. doi: 10.1017/S0022112061000305 [13] Durran D R.Improving the anelastic approximation[J].J Atmos Sci,1989,46(11):1453-1461. doi: 10.1175/1520-0469(1989)046<1453:ITAA>2.0.CO;2 -
计量
- 文章访问数: 2551
- HTML全文浏览量: 131
- PDF下载量: 609
- 被引次数: 0
下载:
渝公网安备50010802005915号