非传统近似下海洋内波的一类WKB近似解

A type of WKB solutions for internal waves under the "non-traditional approximation"

在非传统近似(即,包含地转水平分量在内的完整地转效应)条件下,用WKB(Wentzel–Kramers–Brillouin)方法得到了密度连续分层海洋内波的一类WKB近似解。为了检验所得到的WKB近似解的有效性,对WKB解各垂向速度模态与基于三点中心差分格式及QR算法的数值计算结果进行了详细比对,结果表明,当浮频率N(z)是关于深度z的慢变函数时,WKB近似解与数值结果符合良好。另外,还比较和分析了非传统近似与传统近似条件下内波解的差别,结果表明:地转水平分量一般是不能忽略的,对海洋内波的生成、演变及消衰的研究有着非常重要的意义。

In this paper, a type of WKB（Wentzel-Kramers-Brillouin）approximate analytic solutions was derived by applying the WKB method to the internal waves in continuous density-stratified ocean under the non-traditional approximation, the complete effect of the earth rotation being considered. The vertical velocity modes obtained from the WKB approximate solutions were compared with the numerical results to test the validity of WKB approximate solutions. The study shows that the WKB approximate solutions proposed are consistent with the nu- merical results, when the buoyancy frequency N（z） varies gradually with the ocean depth z. In addition, by comparing the WKB solutions for non-traditional and traditional solutions of internal waves, it is found that the horizantal component of the earth rotation can not be ignored generally. Our results are important to the study of generation, evolution and dissipation of internal waves in the ocean.