Generation of Gravity-Capillary Wind Waves by Instability of a Coupled Shear-Flow

Malek Abid,Yang-Yih Chen,Hung-Chu Hsu,Christian Kharif

doi:10.3390/jmse10010046

Abstract

The theory of surface wave generation, in viscous flows, is modified by replacing the linear-logarithmic shear velocity profile, in the air, with a model which links smoothly the linear and logarithmic layers through the buffer layer. This profile includes the effects of air flow turbulence using a damped mixing-length model. In the water, an exponential shear velocity profile is used. It is shown that this modified and coupled shear-velocity profile gives a better agreement with experimental data than the coupled linear-logarithmic, non smooth profile, (in the air)–exponential profile (in the water), widely used in the literature. We also give new insights on retrograde modes that are Doppler shifted by the surface velocity at the air-sea interface, namely on the threshold value of the surface current for the occurrence of a second unstable mode.

Highlights

An important literature has been devoted to the generation of gravity-capillary waves at the sea surface under the action of a turbulent wind
Ref. [2] investigated the energy transfer from wind to short water waves through the viscous stress in the vicinity of the surface and neglected the shear flow in the water. He suggested that the generation of the short waves is due to a resonance mechanism between the water waves and the Tollmien-Schlichting waves occurring in the air shear flow
We studied surface wave generation by wind in viscous flows

Summary

Introduction

An important literature has been devoted to the generation of gravity-capillary waves at the sea surface under the action of a turbulent wind. The occurrence of gravity-capillary waves has been considered theoretically as the stability of a viscous parallel shear flow of air over water. In the present paper we focus attention on viscous fluids and take into account the shear-induced flow (Figure 1). [2] investigated the energy transfer from wind to short water waves through the viscous stress in the vicinity of the surface and neglected the shear flow in the water. He suggested that the generation of the short waves is due to a resonance mechanism between the water waves and the Tollmien-Schlichting waves occurring in the air shear flow.

Methods

Results

Conclusion