Reappraisal of Whitham's 1967 theory for wave-meanflow interaction in shallow water

被引：4

作者：

Bridges, Thomas J. ^{[1
]}

Ratliff, Daniel J. ^{[2
]}

机构：

[1] Univ Surrey, Dept Math, Guildford GU2 7XH, England

[2] Northumbria Univ, Dept Math Phys & Elect Engn, Newcastle Upon Tyne NE1 8ST, England

来源：

WAVE MOTION | 2022年 / 115卷

关键词：

Whitham modulation theory; Benjamin-Feir instability; Coalescing characteristics; Stokes waves; Wave-mean flow interaction; FINITE-AMPLITUDE; GRAVITY-WAVES; DEEP-WATER; INSTABILITY; MODULATION; PACKETS;

D O I：

10.1016/j.wavemoti.2022.103050

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

The modulation equations for Stokes waves in shallow water coupled to wave-generated meanflow, derived in Whitham (1967), based on an averaged Lagrangian are re-visited. Firstly, it is shown that they can be recast into two coupled classical shallow water equations, with modified gravity having the sign of the Whitham index: sign(omega 0 ''omega 2). Secondly, it is shown that the amplitude of the meanflow and amplitude of the wave are, in general, independent. Thirdly, the implications of the coalescing characteristics, whose unfolding is associated with the Benjamin-Feir instability, are studied.(c) 2022 Published by Elsevier B.V.

引用

页数：14

共 22 条

[1] The spectrum of finite depth water waves [J].

Akers, Benjamin ;

Nicholls, David P. .

EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, 2014, 46 :181-189

[2] INSTABILITY OF PERIODIC WAVETRAINS IN NONLINEAR DISPERSIVE SYSTEMS [J].

BENJAMIN, TB .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1967, 299 (1456) :59-&

[3] Reappraisal of the Kelvin-Helmholtz problem .1. Hamiltonian structure [J].

Benjamin, TB ;

Bridges, TJ .

JOURNAL OF FLUID MECHANICS, 1997, 333 :301-325

[4]

BENNEY DJ, 1969, STUD APPL MATH, V48, P377

[5] Nonlinear Theory for Coalescing Characteristics in Multiphase Whitham Modulation Theory [J].

Bridges, Thomas J. ;

Ratliff, Daniel J. .

JOURNAL OF NONLINEAR SCIENCE, 2021, 31 (01)

[6] Krein signature and Whitham modulation theory: the sign of characteristics and the "sign characteristic" [J].

Bridges, Thomas J. ;

Ratliff, Daniel J. .

STUDIES IN APPLIED MATHEMATICS, 2019, 142 (03) :314-335

[7] A proof of the Benjamin-Feir instability [J].

Bridges, TJ ;

Mielke, A .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1995, 133 (02) :145-198

[8] 3-DIMENSIONAL PACKETS OF SURFACE-WAVES [J].

DAVEY, A ;

STEWARTSON, K .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1974, 338 (1613) :101-110

[9] The instability of periodic surface gravity waves [J].

Deconinck, Bernard ;

Oliveras, Katie .

JOURNAL OF FLUID MECHANICS, 2011, 675 :141-167

[10] 2-DIMENSIONAL PACKETS OF CAPILLARY-GRAVITY WAVES [J].

DJORDJEVIC, VD ;

REDEKOPP, LG .

JOURNAL OF FLUID MECHANICS, 1977, 79 (MAR23) :703-714

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