### 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 N^{2} 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 language | English |
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Pages (from-to) | 606-616 |

Number of pages | 11 |

Journal | Physics of Fluids A |

Volume | 3 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1991 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Physics of Fluids A*,

*3*(4), 606-616. https://doi.org/10.1063/1.858122

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

Research output: Contribution to journal › Article

*Physics of Fluids A*, vol. 3, no. 4, pp. 606-616. https://doi.org/10.1063/1.858122

}

TY - JOUR

T1 - Axisymmetric waves on a vertical vortex in a stratified fluid

AU - Miyazaki, Takeshi

AU - Fukumoto, Yasuhide

PY - 1991/1/1

Y1 - 1991/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0642365901&partnerID=8YFLogxK

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U2 - 10.1063/1.858122

DO - 10.1063/1.858122

M3 - Article

VL - 3

SP - 606

EP - 616

JO - Physics of fluids. A, Fluid dynamics

JF - Physics of fluids. A, Fluid dynamics

SN - 0899-8213

IS - 4

ER -