Wave-current interaction on a free surface
Abstract
The classic evolution equations for potential flow on the free surface of a fluid flow are not closed because the pressure and the vertical velocity dynamics are not specified on the free surface. Moreover, their wave dynamics does not cause circulation of the fluid velocity on the free surface. The equations for free-surface motion we derive here are closed and they are not restricted to potential flow. Hence, true wave-current interaction dynamics can occur. In particular, the Kelvin-Noether theorem demonstrates that wave activity can induce fluid circulation and vorticity dynamics on the free surface. The wave-current interaction equations introduced here open new vistas for both the deterministic and stochastic analysis of nonlinear waves on free surfaces.
Cite
@article{arxiv.2012.12808,
title = {Wave-current interaction on a free surface},
author = {Dan Crisan and Darryl D. Holm and Oliver D. Street},
journal= {arXiv preprint arXiv:2012.12808},
year = {2021}
}
Comments
Refereed version, comments still welcome (please email)