海洋剪切流下失稳内波流场及传播的理论分析

Theoretical analysis on the stream structure and propagation of unstable ocean internal wave at background shear flow

采用求解特征值的方法,探讨了剪切背景流所导致的短波长海洋内波的失稳问题,并给出了其流场结构和传播情况。按照失稳内波波阵面的法向与背景流流向夹角的不同,海洋内波不稳定可分为横波不稳定(夹角为0°),对称不稳定(夹角为90°)和斜交不稳定(任意夹角)3种情况,此时不稳定内波的流场呈现多种形态。对最不稳定流场而言,对称不稳定的流场形态呈现单圈环流的倾斜对流形态,而横波不稳定和斜交不稳定的流场形态则有猫眼结构出现。对于横波不稳定和斜交不稳定内波,最不稳定内波与次不稳定内波两者的流场分布几乎互为镜像。相应于本文的短波长内波,横波不稳定和斜交不稳定的内波均为高频内波,对称不稳定内波不传播,而仅在原地增长。相同参数下垂直方向结构最简单的对称不稳定内波其增长率最大。

The unstable short wavelength ocean internal wave caused by the background shear flow is studied, as well as its stream structure and propagation by using the method of solving eigenvalue. According to the different angle between normal phase front and background flow of unstable wave, there are three types of instability, which are transversal instability （angle of 0 degree）, symmetrical instability （90 degree） and heterotropic instability （arbitrary angle）. Accordingly, the stream field of each unstable ocean internal wave appears differently. To the most unstable stream field, the shape of symmetrically unstable internal wave is a kind of sideling convection with single circle. While the shape of transversally unstable internal wave and heterotropically unstable internal wave appear a cat＇s eye structure. With regard to the transversally unstable internal wave and heterotropically unstable internal wave, the stream fields distribution are nearly mirror images in the most unstable stream field and the second unstable stream field. To the short wavelength internal wave studied in this paper, the transversally and heterotropically unstable internal waves are all in the high frequency. While the symmetrically unstable internal wave cannot propagate but grows only in situ. The symmetrically unstable internal wave with simplest structure has the biggest growing rate on the condition of the same parameters.