The evolution of strongly dispersive internal solitary waves (ISWs) over slope-shelf topography is studied in a two-layer system of finite depth. We consider the high-order vmeKdV model extending the Korteweg-de Vries (KdV) equation with coupling terms of [Formula: see text] order to treat the strong dispersion in the problem which has variable coefficients to adapt the varying bottom topography. The strongly dispersive initial ISW is characterized by the meKdV equation according to the comparison with experiments and can be propagated by the vmeKdV equation according to the comparison between vmeKdV and vKdV theories. The vmeKdV equation is numerically implemented adopting the finite difference scheme. Three dimensionless ISW amplitudes [Formula: see text], 1.136, 1.41 and two slope inclinations [Formula: see text], 1/10 are considered. The deformation of the ISW is observed when a wave propagates past over the slope. The balancing of shoaling effect and energy dispersion determine the amplitude variation. In the cases of mild or steeper slopes, the terminal wave has a stable profile and amplitude, commonly consistent to the meKdV profile with smaller amplitude. In a particular case of mild slope with very small initial amplitude, the terminal wave amplitude grows larger than the original value.

中文翻译：

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斜坡陆架地形上的强色散内孤波变换

在有限深度的两层系统中研究了坡架地形上强色散内部孤立波 (ISW) 的演变。我们考虑使用 [公式：参见文本] 的耦合项扩展 Korteweg-de Vries (KdV) 方程的高阶 vmeKdV 模型，以处理具有可变系数以适应变化的底部地形的问题中的强色散。根据与实验的比较，强色散的初始ISW以meKdV方程为特征，根据vmeKdV和vKdV理论的比较，可以通过vmeKdV方程进行传播。vmeKdV 方程采用有限差分方案在数值上实现。考虑了三个无量纲 ISW 振幅 [公式：见文本]、1.136、1.41 和两个坡度倾角 [公式：见文本]，1/10。当波在斜坡上传播过去时，可以观察到 ISW 的变形。浅滩效应和能量分散的平衡决定了振幅的变化。在斜率较缓或较陡的情况下，终波具有稳定的轮廓和幅度，通常与幅度较小的 meKdV 轮廓一致。在具有非常小的初始幅度的温和斜率的特殊情况下，终波幅度增长大于原始值。