Axisymmetric waves on a vertical vortex in a stratified fluid

Takeshi Miyazaki, Yasuhide Fukumoto

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Axisymmetric wave propagation along a vertical vortex core in a stably stratified fluid is considered theoretically. The fluid is assumed to be inviscid, incompressible, nondiffusive, and exponentially stratified. A linear analysis under the Boussinesq approximation shows that discrete inertial modes (bounded modes) are allowed in addition to continuous internal gravity waves (unbounded modes), when the stratification is not too strong. These inertial modes, whose eigenfunctions are confined to the vorticity region, disappear if the Brunt-Väisälä frequency N2 exceeds the maximum value of the Rayleigh function. Concrete results are given for the Burgers vortex. A weakly nonlinear analysis indicates that inertial modes (if permitted) are generated through the resonant interactions between two internal gravity waves. The time evolution of its amplitude is described by a cubic nonlinear Schrödinger equation, which admits envelope soliton solutions for shorter carrier waves only, viz., the soliton window has a low wave-number cutoff.

Original languageEnglish
Pages (from-to)606-616
Number of pages11
JournalPhysics of Fluids A
Volume3
Issue number4
DOIs
Publication statusPublished - Jan 1 1991
Externally publishedYes

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Gravity waves
Solitons
Vortex flow
Fluids
Nonlinear analysis
Vorticity
Nonlinear equations
Eigenvalues and eigenfunctions
Wave propagation

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Axisymmetric waves on a vertical vortex in a stratified fluid. / Miyazaki, Takeshi; Fukumoto, Yasuhide.

In: Physics of Fluids A, Vol. 3, No. 4, 01.01.1991, p. 606-616.

Research output: Contribution to journalArticle

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