Nonlinear Stability of Localized and Non-localized Vortices in Rotating Compressible Media

Rozanova, Olga; Turzynsky, Marko

doi:10.1007/978-3-319-91548-7_41

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…One can hypothesize that the same phenomenon holds for a localized vortex in a gas, i.e. the instability leads to formation of singularities (see [13]).…”

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confidence: 85%

The Stability of Vortices in Gas on the l-Plane: The Influence of Centrifugal Force

Rozanova

Turzynsky

2019

Springer Proceedings in Mathematics &Amp; Statistics

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We show that a small correction due to centrifugal force usually neglected in the l-plane model of atmosphere drastically influences on the stability of vortices. Namely, in the presence of the Coriolis force only there exists a wide range of parameter ensuring nonlinear stability of a vortex with uniform deformation. Taking into account the centrifugal force results in a disappearance of stable vortices in the above mentioned class of motions.We also prove that for the heat ratio γ = 2, corresponding to the one-atomic gas, the system of equations, describing the gas on the lplane with the correction due to centrifugal force can be integrated in a special case.

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“…One can hypothesize that the same phenomenon holds for a localized vortex in a gas, i.e. the instability leads to formation of singularities (see [13]).…”

mentioning

confidence: 85%

The Stability of Vortices in Gas on the l-Plane: The Influence of Centrifugal Force

Rozanova

Turzynsky

2019

Springer Proceedings in Mathematics &Amp; Statistics

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“…Theorem 2.3. Suppose γ = 2 and there exists a positive T * such that the graphs of functions G(t), given by (16), intersects with φ − (t), given by (14), or with φ + (t), given by (15). Then the classical solution of the Cauchy problem (1) -…”

Section: The Case γ = 2 the Shallow Water Equationsmentioning

confidence: 99%

“…Such functionals are very convenient for studying various properties of a rotating gas (see [10], [11], [14], [15])…”

Section: Introductionmentioning

confidence: 99%

Singularity formation for rotational gas dynamics

Rozanova

2020

Preprint

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The Cauchy problem for the system of equations of two-dimensional rotational gas dynamics is considered. It is assumed that the Cauchy data are a smooth compact perturbation of a constant state. Integral conditions for the data sufficient for the loss of smoothness by a solution within a finite time are found. We analyze the possibility of fulfilling these conditions and compare them with the criterion of singularity formation, known for rotational gas dynamics without pressure.

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A method for constructing special solutions for multidimensional generalization of euler equations with coriolis force

Fan

Yuen

2021

Chinese Journal of Physics

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Nonlinear Stability of Localized and Non-localized Vortices in Rotating Compressible Media

Cited by 4 publications

References 16 publications

The Stability of Vortices in Gas on the l-Plane: The Influence of Centrifugal Force

The Stability of Vortices in Gas on the l-Plane: The Influence of Centrifugal Force

Singularity formation for rotational gas dynamics

A method for constructing special solutions for multidimensional generalization of euler equations with coriolis force

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