On rotational flows with discontinuous vorticity beneath steady water waves near stagnation

TL;DR

This paper numerically studies steady water waves with discontinuous vorticity, revealing complex flow structures, bifurcation behaviors, and detailed pressure and particle trajectory analyses near stagnation points.

Contribution

It introduces new bifurcation branches and provides detailed insights into pressure distributions and particle trajectories for rotational flows with discontinuous vorticity.

Findings

Stagnation points can occur internally, at the bottom, or at the crest.

A new bifurcation branch not connected to trivial solutions is identified.

Pressure distributions and particle trajectories are characterized near stagnation.

Abstract

We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation diagram the stagnation point can first occur internally or at the bottom, and then again occurs at the crest with further increase in wave height. We observe that the bifurcation diagram has a new branch which is not connected to the trivial solution. Furthermore, we present an in-depth discussion of the results on pressure distributions and particle trajectories beneath large-amplitude steady waves near stagnation. We also expand on previous results concerning the amplitude and mass flux of steady water waves traveling on rotational flows with discontinuous vorticity.