Steady water waves in the presence of wind

Samuel Walsh, Oliver Buhler, Jalal Shatah

Research output: Contribution to journalArticle

Abstract

In this paper we develop an existence theory for small amplitude, steady, twodimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin-Helmholtz type discontinuity across the air-water interface, and a corresponding jump in the circulation of the fluids there. We consider both fluids to be inviscid, with the water region being irrotational and of finite depth. The air region is considered with constant vorticity in the case of infinite depth and with a general vorticity profile in the case of a finite, lidded atmosphere.

Original languageEnglish (US)
Pages (from-to)2182-2227
Number of pages46
JournalSIAM Journal on Mathematical Analysis
Volume45
Issue number4
DOIs
StatePublished - 2013

Fingerprint

Water waves
Water Waves
Vorticity
Water
Fluid
Existence Theory
Kelvin
Hermann Von Helmholtz
Air
Atmosphere
Discontinuity
Jump
Fluids
Profile

Keywords

  • Bifurcation theory
  • Traveling waves
  • Water waves
  • Wind wave

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

Steady water waves in the presence of wind. / Walsh, Samuel; Buhler, Oliver; Shatah, Jalal.

In: SIAM Journal on Mathematical Analysis, Vol. 45, No. 4, 2013, p. 2182-2227.

Research output: Contribution to journalArticle

Walsh, Samuel ; Buhler, Oliver ; Shatah, Jalal. / Steady water waves in the presence of wind. In: SIAM Journal on Mathematical Analysis. 2013 ; Vol. 45, No. 4. pp. 2182-2227.
@article{3d52af7818674da9a40ba7210aea8eb0,
title = "Steady water waves in the presence of wind",
abstract = "In this paper we develop an existence theory for small amplitude, steady, twodimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin-Helmholtz type discontinuity across the air-water interface, and a corresponding jump in the circulation of the fluids there. We consider both fluids to be inviscid, with the water region being irrotational and of finite depth. The air region is considered with constant vorticity in the case of infinite depth and with a general vorticity profile in the case of a finite, lidded atmosphere.",
keywords = "Bifurcation theory, Traveling waves, Water waves, Wind wave",
author = "Samuel Walsh and Oliver Buhler and Jalal Shatah",
year = "2013",
doi = "10.1137/120880124",
language = "English (US)",
volume = "45",
pages = "2182--2227",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",

}

TY - JOUR

T1 - Steady water waves in the presence of wind

AU - Walsh, Samuel

AU - Buhler, Oliver

AU - Shatah, Jalal

PY - 2013

Y1 - 2013

N2 - In this paper we develop an existence theory for small amplitude, steady, twodimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin-Helmholtz type discontinuity across the air-water interface, and a corresponding jump in the circulation of the fluids there. We consider both fluids to be inviscid, with the water region being irrotational and of finite depth. The air region is considered with constant vorticity in the case of infinite depth and with a general vorticity profile in the case of a finite, lidded atmosphere.

AB - In this paper we develop an existence theory for small amplitude, steady, twodimensional water waves in the presence of wind in the air above. The presence of the wind is modeled by a Kelvin-Helmholtz type discontinuity across the air-water interface, and a corresponding jump in the circulation of the fluids there. We consider both fluids to be inviscid, with the water region being irrotational and of finite depth. The air region is considered with constant vorticity in the case of infinite depth and with a general vorticity profile in the case of a finite, lidded atmosphere.

KW - Bifurcation theory

KW - Traveling waves

KW - Water waves

KW - Wind wave

UR - http://www.scopus.com/inward/record.url?scp=84888881431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888881431&partnerID=8YFLogxK

U2 - 10.1137/120880124

DO - 10.1137/120880124

M3 - Article

AN - SCOPUS:84888881431

VL - 45

SP - 2182

EP - 2227

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 4

ER -