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一、引 言 十多年来,用摄动法研究非线性波已经取得了相当大的成就.在流体力学方面研究较多的是浅水表面波,在大气科学方面研究较多的是Rossby波.对层结流体中的内波,则研究较少.大家知道,海洋和大气都是密度随深度或高度变化的层结(分层)流体.许多重要的自然现象,如台风、飑线、积云、湍流、海洋中的温跃层等,都和重力内波有关.随着卫星技术的发展,非线性重力内波已经在大气和海洋中观测到.从理论上研究非线性重力内波较早的是Benney(1966)和Benjamin(1966,1967),最近Ma-slowe和Redekopp(1980)对层结剪切流动的非线性内波作了系统详细的研究.但是,所有这些研究都是采用多尺度摄动法和约化摄动法.这种方法比较烦琐,虽然非线性内波
I. INTRODUCTION For more than a decade, quite a lot of achievements have been made in the study of non-linear waves by perturbation method. There are many studies on hydrodynamics in shallow water surface waves and Rossby waves in atmospheric science. There are few studies on the internal waves in stratified fluids, and it is well known that both the ocean and the atmosphere are stratified (stratified) fluids whose density varies with depth or height and that many important natural phenomena such as typhoons, rays, cumulus , Turbulence, the thermocline in the ocean and so on are all related to the internal gravity waves.With the development of satellite technology, the nonlinear gravity internal waves have been observed in the atmosphere and the ocean.Studying the nonlinear gravity internal waves earlier Benney (1966) and Benjamin (1966, 1967), and Ma-slowe and Redekopp (1980) recently performed a detailed study of the nonlinear shear waves in laminar shear waves. However, all of these studies use more Scale perturbation method and reduction perturbation method.This method is more cumbersome, although the nonlinear internal wave