Pressure anomalies beneath solitary waves with constant vorticity

TL;DR

This paper numerically investigates the pressure distribution beneath solitary waves with constant vorticity, revealing threshold effects on pressure anomalies and stagnation points depending on vorticity strength.

Contribution

It introduces a novel numerical method using conformal mapping to analyze pressure and velocity fields beneath such waves, filling a gap in existing research.

Findings

Pressure anomalies occur above a certain vorticity threshold.

Multiple stagnation points appear when vorticity exceeds the threshold.

Pressure distribution varies significantly with vorticity strength.

Abstract

While some works 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 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.