非均匀非平稳分层介质中重力波的动力学
Dynamics of the internal gravity waves in the heterogeneous and nonstationary stratified mediums
摘要：
本文在垂直分层介质参数在水平方向上随时间变化缓慢的假设下，分析了重力波的非简谐波列的演化。波列的特殊形式可以用一些特殊的函数来表示，如Airy函数、Fresnel积分、Pearsy积分等，并且由相应奇点附近的分离模式的色散曲线的局部行为确定。利用作者提出的改进的时空射线追踪方法，可以解决这一问题（射线光学的方法），其根本区别在于，这种解决方案的渐近符号应该使用一些小参数的非整数阶以级数的形式搜索，在分层非平稳水平非均匀介质中存在的非简谐波列的演化分析中，以使用某个小参数的非整数度的级数形式搜索解的渐近形式，此时，指数取决于波列符号的具体类型。该符号的具体形式是由稳态水平均匀事件中解的渐近行为确定的。波列的相位将由相应的程函方程确定，程函方程可以使用特征（射线）进行数值求解。波列的振幅由沿特征（射线）的某种守恒定律确定。
英文摘要：
In the present paper in the assumption of the slowness of variation of the vertically stratified medium parameters in the horizontal direction within the time we have analyzed the evolution of the non-harmonic wave trains of the internal gravity waves. The particular form of the wave train can be expressed through some special functions, for example, Airy functions, Fresnel integrals, Pearsy integrals, etc., and is determined by the local behavior of the dispersion curves of the separate modes near to the corresponding singular points. The solution of this problem is possible using the modified version of the space-time ray-tracing method offered by the authors (the method of the ray optics), the fundamental difference of which consists, that the asymptotic notation of such a solution should be searched for in the form of the series using the non-integral degrees of some small parameter, the asymptotic forms of the solution at analysis of evolution of the non-harmonic wave trains present in the stratified non-stationary horizontally-non-uniform mediums is searched in the form of the series using the non-integral degrees of some small parameter, at that the exponent depends on the concrete type of the wave train notation. The particular form of the notation is determined from the asymptotical behavior of the solution in the stationary horizontally-homogeneous event. The phase of the wave train will be determined from the corresponding eikonal equation, which can be solved numerically using the characteristics (rays). The amplitude of the wave train is determined from some law of preservation along the characteristics (rays).
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