Rotational Solitary Wave Interactions over an Obstacle

AUTOR(ES)

FLAMARION, M. V.

FONTE

Trends in Computational and Applied Mathematics

DATA DE PUBLICAÇÃO

2022

RESUMO

ABSTRACT In this work, we investigate the propagation of rotational solitary waves over a submerged obstacle in a vertically sheared shallow water channel with constant vorticity. In the weakly nonlinear, weakly dispersive regime the problem is formulated in the forced Korteweg-de Vries equation framework. The initial value problem for this equation is solved numerically using a Fourier pseudospectral method with an integrating factor. Solitary waves are taken as initial data and their interactions with an obstacle are analysed. We identify three types of regimes according to the intensity of the vorticity. A rotational solitary wave can bounce back and forth over the obstacle remaining trapped for large times, it can pass over the obstacle without reversing its direction or the wave can be blocked, i.e., it bounces back and forth above the obstacle until reaching a steady state. Such behaviour resembles the classical damped spring-mass system.

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