Wave growth by non-separated sheltering
type: Item
instance of: scholarly article
title: Wave growth by non-separated sheltering
zbMATH Open document ID: 0961.76012
DOI: 10.1016/S0997-7546(99)80041-7
author: Stephen E. Belcher
published in: European Journal of Mechanics. B. Fluids
publication date: 2001-05-20T00:00:00Z
review text: \textit{H. Jeffreys} (1925) put forward the sheltering mechanism of wind-induced growth of surface water waves, whereby the air flow was assumed to separate in the lee of the wave crest, leading to a pressure difference across the wave crests, and thus to wave growth. Jeffreys found the wave growth rate in terms of an undetermined parameter, which he called sheltering coefficient. Most ocean waves have gentle slopes without separation, and recent studies show how for these gentle waves turbulent stresses in air flow lead to a reduction in wind speed in the lee, so that streamlines reach their maximal vertical displacement slightly downwind of the wave crest. There is an associated pressure difference across the wave, and hence an associated wave growth. In other words, for waves of small slope and without separation, there is a non-separated sheltering that leads to the growth of waves. This mechanism, which is associated with turbulence in the wind, complements the celebrated critical-layer mechanism of wave growth first analyzed by \textit{J. W. Miles} [J. Fluid Mech. 30, 163-175 (1967; Zbl 0153.30303)], which is an inviscid shear-flow instability. There have been studies of how the non-separated sheltering and the critical-layer mechanisms act together, but no definitive conclusions have been reached. The detailed and rigorous analyses of non-separated sheltering over slow waves and fast waves are mathematically difficult. The purpose of this paper is to develop a more heuristic method, with no intention of rigor, but which sheds light on the physical processes responsible for non-separated sheltering. The method is based on analyzing the displacement of streamlines over the wave, and is based on the elegant formalism introduced by \textit{J. W. Miles} [J. Fluid Mech. 256, 427-441 (1993)]. The present study can be considered as a step towards analyzing together the effects of non-separated sheltering and the critical layer. The solutions obtained here using physi…
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 1358007
zbMATH Keywords: wind-induced growth of surface waver waves
zbMATH Keywords: non-separated sheltering
zbMATH Keywords: sheltering mechanism
zbMATH Keywords: gentle waves
zbMATH Keywords: inviscid shear-flow instability
zbMATH Keywords: critical-layer mechanism
zbMATH Keywords: streamlines
reviewed by: Leonid B. Chubarov
MaRDI profile type: Publication
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Wikidata QID: Q127293562
description: scientific article; zbMATH DE number 1358007