大气波动的波谱和谱函数——垂直切变基流中的波谱分析

Spectrum and Spectral Function of Wave in Atmosphere——Wave Spectrum Analysis with Vertical Shear of Basic Flow

作者研究了具有垂直切变基流时大气波动连续谱的重叠问题和临界层出现的情况。发现随着基流切变的增大和扰动波长的减小,一支涡旋波和两支重力惯性内波的连续谱区会互相靠拢,最后发生重叠,这时已不能区分为快波、慢波,而能否重叠的关键在于临界波长与扰动波长的相对大小,基流切变越大,扰动波长越短,重叠现象就越严重。这可用作划分运动尺度的客观标准。当运动尺度大于临界波长时,是大尺度的,这时三支波动连续谱区互相不重叠,涡旋波是准地转的;当运动尺度小于临界波长时,可认为是中尺度的,此时出现连续谱重叠现象。采用该方法划分的尺度标准与通常的标准在量级上则相一致。

As one of basic researches in the mesoscale system, it is necessary to make 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 which 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-geostatic quasi-two-dimensional Boussinesq equations. It is supposed that basic flow is only the function of z. The equations are linearized under definite conditions, and then initial-boundary value problem is changed into eigenvalue problem of generalized matrix after assuming normal mode solution. The characteristics of spectrum and spectral function can be realized. In this paper, the problem on overlapping of the continuous wave spectrums and the instance on appearance of the critical layer are studied in atmosphere with the shear of basic flow. The results can be concluded as follows. There are three waves in the equations., a couple of internal inertial-gravitational wave and a vortex wave. These three waves all have continuous spectrum and critical layers. When the shear increases and the wavelength decreases, it is found that the continuous spectrum region of a branch of vortex wave is close to the region of a couple of internal inertial-gravitational wave, they shall overlap each other finally. Here fast wave cannot be distinguished from slow wave. The overlapping condition is determined by the scales of critical wavelength and perturbation wavelength. When the disturbance wavelength is less than the critical wavelength and greater than half of that, there exists the overlapping section of an internal inertial-gravitational wave and a vortex wave. And when the disturbance wavelength is less than the half of critical wavelength, there exists the overlapping section of three waves. Here, there is not pure continuous spectrum section of the vortex wave. The critical wavelength can be considered as the criterion of dividing scale of atmosphere motion. When the scale of motion is greater than the critical wavelength, it is large scale. Here the continuous spectrum regions of the vortex wave and the internal inertialgravitational wave do not overlap, and the vortex wave is quasi-geostrophic. When the scale of motion is less than the critical wavelength, it is mesoscale. Here the overlapping of the continuous spectrum regions occurs. The standard is identical with accustomed standard in magnitude.