论小尺度过程动力学的一些基本问题

ON SOME FUNDAMENTAL PROBLEMS OF DYNAMICS OF SMALL SCALE PROCESSES IN THE ATMOSPHERE

中文摘要:

      本文对层结大气中小尺度过程动力学的一些基本问题作了研究。首先用频率法对线性化后的小尺度运动方程作了分析。分析指出,线性化后的运动方程中包含了两种不同类型的波动,即快速传播的声波和相对声波而言的慢波——重力内波。对于有气象意义的运动而言,声波是一种"噪音",必须从运动方程中把它滤掉。文中指出,由于静力偏差(非静力平衡)对小尺度运动的发展具有重要的意义,一般用静力平衡来消除声波的方法对小尺度运动并不适用。文中提出了三种不同的消除声波的方法,即1)不可压缩条件的应用;2)将解按参数ε'(=V²/gL)的冪次展开;3)平衡方程的应用。同时分析了这三种不同滤波方法所带来的误差程度。作为初值问题,研究了当在某一时刻在大气有限区域内的扰动破坏了静力平衡后所激发出的声波的频散性质,指出,从静力平衡的破坏到其种平衡状态的建立,场的这一适应过程完成得极其迅速。最后,利用所提出的滤波方法,建立了滤掉声波后的二维非线性运动方程组。

英文摘要:

      In the present paper,the properties of the solutions of the linearized equations of the small scale processes are analysed by the frequency method.It is indicated that there are two basic types of dynamical processes which correspond to those of the sound and the gravitational waves.In general,the rapid sound wave does not correspond to the meteorologically significant phenomena and.the existance of that wave will distort the actual changes connected with the meteorologically significant motion.Therefore,it is necessaiy to filter the sound wave from the equations of small scale motion.It is indicated that the static departure(static unequilibrium) is important for the development of small scale processes,such as the convection,so that it is not permitted to use the static approximation to filter the internal sound Wave.In this paper,for filtering the sound wave tliree methods are introduced,namely,1) applicationof imcompressiblibity;2) the solution in power series of the small parameter's,the Froude number,and 3) application of the balance equation for the small scale process.The error introduced by each of these methods is also analysed.