热带气旋解析解与数值解的比较  

Comparison between analytical and numerical solutions of tropical cyclone perturbation

作　　者：赵艳玲[1,2] 刘琳[1] 张铭[1] 

机构地区：[1]解放军理工大学气象学院大气环流与短期气候预测实验室,南京211101 [2]解放军91876部队,河北秦皇岛066203

出　　处：《气象科学》2009年第3期381-385,共5页Journal of the Meteorological Sciences

基　　金：国家自然科学基金资助项目(40575023)

摘　　要：对热带气旋波谱分析正确性的验证进行了讨论。通常可找一个能解析求解的特例,并对该特例求数值解,然后比较两者的结果。在保证解析解正确的前提下,若两者结果不一致,则数值求解肯定有问题。这里给出了热带气旋波谱分析验证的具体步骤,还求得了基流趋于零时热带气旋尺度涡旋中正压原始方程特征值问题的解析解。通过比较解析解和数值解的频率可知,两者的差别并不大,最大相对误差小于10%。这表明数值计算的方案设计和编程至少在基流趋于0时是没有问题的。此时仅存在一对重力惯性波,并得到了其频率方程,其特征函数可用Bessel函数来表示。因该函数是基流趋于0情况下扰动的解,故其不可能再是典型基流下的解。该情形下求取数值解看来是唯一的办法。The verification of wave spectrum analysis program about tropical cyclone is discussed. In general, a special case that can be solved analytically is numerically solved, and then the numerical solution and the analytical solution are compared. If we guarantee the analytical solution is right, the numerical solution must be wrong if the two results are different. In this paper, the specific verification process is given for wave spectrum analysis of disturbance in tropical-cyclone-scale vortex. In addition, the eigen- value problem of barotropic primitive equation in tropical-cyclone-scale vortex is analytically solved when the basic flow tends to zero. By comparison, we can see that there is little difference between the numerical solution and the analytical solution, and the largest relative error is less than 10%. It shows that the numerical calculation is right in this case. Here only a pair of gravity inertial waves exist. The eigenfunction of the frequency equation can be expressed by Bessel function, which is right only when the basic flow tends to zero. So in order to gain the solution in the typical flow, we have to turn to the numerical way.

关 键 词：热带气旋 解析解 数值解 BESSEL函数 

分 类 号：P457.8[天文地球—大气科学及气象学]