The propagation of internal undular bores over variable topography

PHYSICA D-NONLINEAR PHENOMENA

卷:333

Article; Proceedings Paper

Grimshaw, R.¹  Yuan, C.¹ 

[1] UCL, Dept Math, London, England

关键词: Whitham modulation theory;    Undular bores;    Internal waves change of polarity;   

DOI  :  10.1016/j.physd.2016.01.006

来源: Elsevier

【 摘 要 】

In the coastal ocean, large amplitude, horizontally propagating internal wave trains are commonly observed. These are long nonlinear waves and can be modelled by equations of the Korteweg-de Vries type. Typically they occur in regions of variable bottom topography when the variable-coefficient Korteweg-de Vries equation is an appropriate model. Of special interest is the situation when the coefficient of the quadratic nonlinear term changes sign at a certain critical point. This case has been widely studied for a solitary wave, which is extinguished at the critical point and replaced by a train of solitary waves of the opposite polarity to the incident wave, riding on a pedestal of the original polarity. Here we examine the same situation for an undular bore, represented by a modulated periodic wave train. Numerical simulations and some asymptotic analysis based on Whitham modulation equations show that the leading solitary waves in the undular bore are destroyed and replaced by a developing rarefaction wave supporting emerging solitary waves of the opposite polarity. In contrast the rear of the undular bore emerges with the same shape, but with reduced wave amplitudes, a shorter overall length scale and moves more slowly. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free