摘要
作者得到了准二维Boussinesq方程组,并用其研究了中尺度大气波动的波谱和谱函数。在一定条件下对该方程组线性化并取标准模后,可将其初边值问题转化为矩阵的广义特征值问题来进行数值求解,这样就可知原问题波谱和谱函数的性质。当无基本流且取地转参数、层结参数为常数时,可求得其波谱和谱函数的解析解。此时该模式中仅包含有一对重力惯性内波模态,且各模态均是简谐波;模态越高,垂直波数越大则波动传播得越慢,所有的模态均为离散谱,并存在聚点。对此作者用数值解作了验算,结果表明,该数值求解方案合理可行,对不太高的模态其精度也令人满意。在无基本流然而考虑层结的垂直变化后,则一般无法求取解析解,为此进行了数值求解。这时该模式仍仅包含有一对重力惯性内波的离散谱模态,不过由于层结参数的变化,各模态结构与简谐波出现了偏差。
As one of basic researches in the mesoscale system, it is necessary to made clear the waves and their characteristics in the mesoscale system. But, what are characteristics of the vortex wave and the inertia-gravitational wave？ Do they have separability？ All these are the new problems that need to be solved urgently. So in this paper the authors try to answer the questions. The spectrum and spectral function of the mesoscale wave are studied by using non-static equilibrium quasl-two-dimensional Boussinesq equations. It is supposed that the basic flow is only the function of z. The equations of are linearized under definite conditions, and then the initial and boundary value problem is changed into the eigenvalue problem of generalized matrix after assuming normal mode solution. The characters of spectrum and spectral function can be realized. And conclusions can be got as follows. When the basic flow is zero and the stratification parameter and the Coriolis parameter are constant, it is easy to get analytical solution of the spectra and spectral function. In this circumstance, only a couple of internal inertial gravity waves exist and all kinds of modes are simple harmonic wave. The higher mode is, the slower the wave travels and the greater the vertical wave number is. All modes are discrete spectrum, and there are accumulation points. In addition, checking numerical computation is discussed. It is shown that the scheme of numerical calculation is reasonable and the precision of numerical calculation is higher in lower mode. If a variety of vertical stratification structure is considered, in general, the analytical solution of eigenvalue problem cannot be gotten, even no basic flow. Accordingly, the numerical solutions are applied. Here only discrete spectrum of the internal inertial gravity wave exists, and as the stratification parameter changes, the structures of mode deviate from that of simple harmonic wave. When the basic flow is not equal to zero, the question becomes more complex. And there are three
出处
《大气科学》
CSCD
北大核心
2007年第4期666-674,共9页
Chinese Journal of Atmospheric Sciences
基金
国家自然科学基金资助项目40575023
关键词
中尺度波动
波谱
谱函数
mesoscale wave, wave spectrum, spectral function
