| 中尺度大气波动的波谱和谱函数——数学模型和计算方法 |
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| 引用本文： | 张铭,安洁.中尺度大气波动的波谱和谱函数——数学模型和计算方法[J].大气科学,2007,31(4):666-674. |
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| 作者姓名： | 张铭 安洁 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金资助项目40575023 |
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| 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。
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| 关 键 词： | 中尺度波动 波谱 谱函数 |
| 文章编号： | 1006-9895（2007）04-0666-09 |
| 修稿时间： | 2006-01-042006-05-08 |
Spectrum and Spectral Function Analysis of Mesoscale Wave——Mathematic Model and Numerical Calculation Method |
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| ZHANG Ming and AN Jie.Spectrum and Spectral Function Analysis of Mesoscale Wave——Mathematic Model and Numerical Calculation Method[J].Chinese Journal of Atmospheric Sciences,2007,31(4):666-674. |
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| Authors: | ZHANG Ming and AN Jie |
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| Institution: | Laboratory of Atmospheric Circulation and Short-range Climate Forecast Meteorological College, PLA University of Science and Technology, Nanjing 211101 |
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| Abstract: | 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 quasi-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 waves in the equations: a couple of internal inertial gravity waves and a vortex wave.These three waves all have continuous spectrum,critical layer and the critical wavelength which depend on the geostrophic parameter f and the vertical shear of basic flow.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 gravity wave and a vortex wave.And when the disturbance wavelength is less than half of the critical wavelength,there exists the overlapping section of the three waves.Here,there is no pure continuous spectrum section of the vortex wave,and the fast wave or the slow wave cannot be distinguished.The critical wavelength can be considered as the criterion of dividing scale of atmosphere motion. |
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| Keywords: | mesoscale wave wave spectrum spectral function |
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