Free surface water-waves generated by instability of an exponential shear flow

TL;DR

This paper investigates the stability of exponential shear flows in water, focusing on gravity and capillarity effects, and presents new insights into gravity-capillary wave generation in finite depth conditions.

Contribution

It provides novel results on gravity-capillary wave generation and extends previous stability analyses to include larger-scale perturbations in exponential shear flows.

Findings

New results on gravity-capillary wave generation

Extended stability analysis to larger-scale perturbations

Insights into exponential shear flow stability in finite depth

Abstract

The stability of an exponential current in water to infinitesimal perturbations in the presence of gravity and capillarity is investigated. Some new results on the generation of gravity-capillary waves are presented which supplement the previous works of Morland, Saffman \& Yuen (1991) and Young \& Wolfe (2014), namely in finite depth. To consider perturbations of much larger scales, a specific attention is paid to the stability of the exponential current only in the presence of gravity.