Abstract

A method for determining the background parameters of weakly dispersive media based on the theory of low-intensity undular bores in such media is proposed. An analytical model of an undular (cnoidal) bore on a pycnocline of a stratified shallow sea is used to obtain expressions for calculating the coefficients of the extended Korteweg–de Vries equation: the velocities of linear internal waves, high-frequency dispersion, quadratic and cubic nonlinearities, i.e., the parameters characterizing the hydrophysical background over which the bore propagates. These parameters are calculated from data of direct measurements of bore characteristics: their wave records, nonlinear velocity, “mass" and amplitude of leading solitons, and the frequencies of the rear waves in the region of bore propagation. The efficiency of the proposed method is confirmed by the results of numerical simulation.

中文翻译：

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弱分散分层浅水背景参数的确定

摘要

提出了一种基于弱强度介质孔洞理论的弱分散介质背景参数确定方法。使用分层浅海比诺斜面上的波浪状（正弦）孔的解析模型来获得表达式，以计算扩展的Korteweg-de Vries方程的系数：线性内波的速度，高频色散，二次波和三次非线性，即表征孔扩展的水文物理背景的参数。这些参数是根据直接测量孔特征的数据计算得出的：其波记录，非线性速度，超前孤子的“质量”和振幅以及孔传播区域中后波的频率。