| Analytical investigation on 3D non-Boussinesq mountain wave drag for wind profiles with vertical variations |
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| 作者姓名： | 唐锦赟 汤杰 王元 |
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| 作者单位： | Department of Atmospheric Science Key Laboratory of Mesoscale Severe Weather of Ministry of Education，Nanjing University，Department of Atmospheric Science，Key Laboratory of Mesoscale Severe Weather of Ministry of Education，Nanjing University，Department of Atmospheric Science，Key Laboratory of Mesoscale Severe Weather of Ministry of Education，Nanjing University，Nanjing 210093，P.R.China，Nanjing 210093，P.R.China，Nanjing 210093，P.R.China |
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| 基金项目： | 国家重点基础研究发展计划(973计划);国家自然科学基金 |
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| 摘 要： | 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 is 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) are 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 that 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 deceases with height). This difference is evident whenever the model is hydrostatic or not.
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| 关 键 词： | 三维非Boussinesq剪切流 重力波阻 风廓线 垂直变异 分析模型 圆钟形山体 风切变 |
| 收稿时间： | 2005-10-18 |
| 修稿时间： | 2006-10-31 |
Analytical investigation on 3D non-Boussinesq mountain wave drag for wind profiles with vertical variations |
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| Tang Jin-yuan,Tang Jie,Wang Yuan.Analytical investigation on 3D non-Boussinesq mountain wave drag for wind profiles with vertical variations[J].Applied Mathematics and Mechanics(English Edition),2007,28(3):317-317. |
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| Authors: | Tang Jin-yuan Tang Jie Wang Yuan |
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| Institution: | Department of Atmospheric Science,Key Laboratory of Mesoscale Severe Weather of Ministry of Education,Nanjing University,Nanjing 210093,P.R.China |
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| 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 is 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) are 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 that 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 deceases with height). This difference is evident whenever the model is hydrostatic or not. |
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| Keywords: | gravity wave drag (GWD) wind shear Wentzel-Kramers-Brillouin (WKB)approximation circular bell-shaped mountain |
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