A new analytical model was developed to predict the gravity wave drag （GWD） induced by an isolated 3-dimensional mountain, over which a stratified, nonrotating non-Boussinesq sheared flow is impinged. The model is c...A new analytical model was developed to predict the gravity wave drag （GWD） induced by an isolated 3-dimensional mountain, over which a stratified, nonrotating 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, itwas 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.展开更多
When the magnitude of sub-scale ographic forcing is comparable with explicitly ordinary dynamic forcing, the drag effect reduced by ographic gravity wave is to be significant for maintaining dynamic balance of atmosph...When the magnitude of sub-scale ographic forcing is comparable with explicitly ordinary dynamic forcing, the drag effect reduced by ographic gravity wave is to be significant for maintaining dynamic balance of atmospheric circulation, as well as the momentum and energy transport. Such sub-scale ographic forcing should be introduced into numerically atmospheric model by means of drag being parameterized. Furthermore, the currently mature ographic gravity wave drag （OGWD） parameterization, i.e., the so-called first-generation （based on lineal single-wave theoretical framework） or the second-generation drag parameterization （including an important extra forcing by the contribution of critical level absorption）, cannot correctly and effectly describe the vertical profile of wave stress under the influence of ambient wind shearing. Based on aforementioned consideration, a new two-wave scheme was proposed to parameterize the ographic gravity wave drag by means of freely propagating gravity waves. It starts with a second order WKB approximation, and treats the wave stress attenuations caused by either the selective critical level absorption or the classical critical level absorption explicitly; while in the regions where critical levels are absent, it transports the wave stress vertically by two sinusoidal waves and deposits them and then damps them according to the wave saturation criteria. This scheme is thus used to conduct some sample computations over the Dabie Mountain region of East China, as an example. The results showed that the new two-wave scheme is able to model the vertical distribution of the wave stress more realistically.展开更多
基金Project supported by the National Basic Research Program of China (973 Program) (No.2004CB418301)the National Natural Science Foundation of China(Nos.40575017 and 40333031)
文摘A new analytical model was developed to predict the gravity wave drag （GWD） induced by an isolated 3-dimensional mountain, over which a stratified, nonrotating 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, itwas 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.
基金the State Natural Science Foundation of China under Grant Nos.40775034,40575017,and 90715031the Natural Science Foundation of Jiangsu under Grant No.BK99020the open project of State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences.
文摘When the magnitude of sub-scale ographic forcing is comparable with explicitly ordinary dynamic forcing, the drag effect reduced by ographic gravity wave is to be significant for maintaining dynamic balance of atmospheric circulation, as well as the momentum and energy transport. Such sub-scale ographic forcing should be introduced into numerically atmospheric model by means of drag being parameterized. Furthermore, the currently mature ographic gravity wave drag （OGWD） parameterization, i.e., the so-called first-generation （based on lineal single-wave theoretical framework） or the second-generation drag parameterization （including an important extra forcing by the contribution of critical level absorption）, cannot correctly and effectly describe the vertical profile of wave stress under the influence of ambient wind shearing. Based on aforementioned consideration, a new two-wave scheme was proposed to parameterize the ographic gravity wave drag by means of freely propagating gravity waves. It starts with a second order WKB approximation, and treats the wave stress attenuations caused by either the selective critical level absorption or the classical critical level absorption explicitly; while in the regions where critical levels are absent, it transports the wave stress vertically by two sinusoidal waves and deposits them and then damps them according to the wave saturation criteria. This scheme is thus used to conduct some sample computations over the Dabie Mountain region of East China, as an example. The results showed that the new two-wave scheme is able to model the vertical distribution of the wave stress more realistically.
