Pressure Anomalies Beneath Solitary Waves with Constant Vorticity

Abstract

While some studies have investigated the particle trajectories and stagnation points beneath solitary waves with constant vorticity, little is known about the pressure beneath such waves. To address this gap, we investigate numerically the pressure beneath solitary waves in flows with constant vorticity. Through a conformal mapping that flats the physical domain, we develop a numerical approach that allows us to compute the pressure and the velocity field in the fluid domain. Our experiments indicate that there exists a threshold vorticity such that pressure anomalies and stagnation points occur when the intensity of the vorticity is greater than this threshold. Above this threshold, the pressure on the bottom boundary has two points of local maxima and there are three stagnation points in the flow, and below it the pressure has one local maximum and there is no stagnation point.