三层模式背风波的理论研究

THEORETICAL STUDY ON TRAPPED LEE WAVES ON THREE-LAYERS MODEL

文中建立了一个背风波的三层理论模式 ;当三层Scorer参数在中层最大、高层次之、下层最小的情况下 ,利用该模式求得了背风波的理论波长及扰动的解析解 ,并对一个典型的个例计算了其背风波波长 ,并在此基础上分析了背风波波长对上、中、下三层Scorer参数变化的敏感性 ,结果表明波长对中层Scorer参数的变化比较敏感 ,对下层Scorer参数的大小和符号都不敏感 ,但在计算背风波波长时不能忽略下层的Scorer参数。

Under certain conditions, airflow over a mountain can force trapped lee waves. Scorer (1949) first introduced the Scorer parameter (l2) into a two-layer model, and lead to the necessary condition for trapped lee waves. Since then, lots of investigations have been based on the two-layer model. However, the Scorer parameter in the real atmosphere is complex, and the two-layer model is highly limited on dealing with actual questions. It is well known that the distribution of stratification (N2) often appears in such a pattern, in which a very small even negative value in the boundary layer, a larger value in the midtropospheric stable layer, and a smaller value again in upper troposphere. If the horizontal wind speed change with height is not sharp, the Scorer parameter will satisfy l2 1≤l2 3<l2 2, l2 1, l2 2 and l2 3, are Scorer parameters in the low, middle and upper layers, respectively. In this paper, a theoretic model of this kind of lee waves was established. Using this model, the theoretical wavelength and the analytic disturbance solution of the trapped lee waves were obtained. Then, the trapped lee wavelength of an idealized three-layer case was calculated, on the base of the work that the sensitivity of the wavelength to Scorer parameters in every layer was analyzed. The result showed that the sensitivity to the Scorer parameter in middle layer was the most remarkable, and the value and sign of that in lower layer were all not very sensitive. In order to compare the three-layer model with the two-layer model, the three-layer case was translated into three two-layer cases by use of different methods. The calculation results showed that the wavelengths of these three cases were very different from that of the three-layer case. It is suggested that the Scorer parameter in lower layer can't be ignored when the trapped lee wavelength is calculated. The calculating streamlines in the three-layer model revealed that the strongest disturbance located in the middle layer, which was consistent with the observational result. In addition, a particular three-layer case was calculated, in which the Scorer parameter of the lower layer was negative. The results showed that the structure of streamline disturbance changes less than that of the former three-layer model.