Stationary gravity waves with the zero mean vorticity in stratified fluid

Clamond, D. and Stepanyants, Y. (2012) Stationary gravity waves with the zero mean vorticity in stratified fluid. Studies in Applied Mathematics, 128 (1). pp. 59-85. ISSN 0022-2526


A new approach to the description of stationary plane waves in ideal density stratified incompressible fluid is considered without application of the Boussinesq approximation. The approach is based on the Dubreil-Jacotin–Long equation with the additional assumption that the mean vorticity of the flow is zero. It is shown that in the linear approximation the spectrum of eigenmodes and corresponding dispersion equations can be found in closed analytical forms for many particular relationships between the fluid density and stream function. Examples are presented for waves of infinitesimal amplitude. Exact expression for the velocity of solitary wave of any amplitude is derived.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Article first published online: 16 DEC 2011. Permanent restricted access to published version due to publisher copyright policy. The definitive version is available at
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 05 May 2012 01:50
Last Modified: 19 Jan 2015 23:24
Uncontrolled Keywords: gravity waves; internal waves; vorticity; stratified fluid; dispersion relation; linear approximation; stationary waves
Fields of Research : 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
02 Physical Sciences > 0201 Astronomical and Space Sciences > 020105 General Relativity and Gravitational Waves
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
Identification Number or DOI: 10.1111/j.1467-9590.2011.00530.x

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