Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256331 | Physica D: Nonlinear Phenomena | 2016 | 8 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
R. Grimshaw, C. Yuan,