Trapped solitary-wave interaction for Euler equations with low-pressure region

Abstract

Trapped solitary-wave interaction is studied under the full Euler equations in the presence of a variable pressure distribution along the free surface. The physical domain is flattened conformally onto a strip and the computations are performed in the canonical domain. Computer simulations display solitary waves that remain trapped in a low-pressure region. In terms of confinement, we observe that these waves are stable for small perturbations of either their amplitudes or the pressure forcing term. Furthermore, multiple solitary waves are considered within the low-pressure region without escaping the low-pressure region. We identify regimes in which multiple solitary waves remain trapped after several collisions. In particular, we display a regime where three solitary waves are trapped and collide several times, before one escapes at a time. The remaining solitary waves stay trapped in the low-pressure region.