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The stability of vortices in gas on the l-plane: the influence of centrifugal force
P. 131–143.
Rozanova O. S., Turtsynskiy M.
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 l-plane with the correction due to centrifugal force can be integrated in a special case.
Shikanian A., Parfenyev V., Physics of Fluids 2025 Vol. 37 No. 9 Article 095127
We study two-dimensional turbulence in a square no-slip domain without bottom drag using direct numerical simulations. The dynamics are shown to depend strongly on the torque $M$ of the external forcing. When $M$ is relatively large, a long-lived coherent vortex forms at the domain center, establishing a persistent angular momentum. At lower torques, the angular ...
Added: September 6, 2025
Springer, 2024.
This book provides a state-of-the-art review of Pilot Wave Theory at the beginning of the XXI century. It contains the best contributions of the first International Conference on Advances in Pilot Wave Theory, held in Lisbon in 2021. The event brought together physicists from the new emerging field of Hydrodynamic Quantum Analogs (HQA) and philosophers ...
Added: September 9, 2024
Papatryfonos K., Vervoort L., Nachbin A. et al., Physical Review Fluids 2024 Vol. 9 No. 8 Article 084001
Since its discovery in 2005, the hydrodynamic pilot-wave system has provided a concrete macroscopic realization of wave-particle duality and concomitant classical analogs of a growing number of quantum effects. The question naturally arises as to how closely particle-particle correlations achieved with this classical system can mimic those arising on the quantum scale. We here introduce ...
Added: August 29, 2024
Rozanova O. S., Turtsynskiy M., , in: Application of mathematics in technical and natural sciences. AIP conference proceedings.Vol. 2164.: AIP Publishing LLC, 2019.
Added: October 31, 2021
Shilin I., Доклады Академии наук 2016 Т. 469 № 3 С. 287–290
В работе показано, что неустойчивость аттракторов Милнора по Ляпунову является локально топологически типичным динамическим явлением, которое наблюдается в присутствии устойчивых гомоклинических касаний для 2-сжимающих периодических седел. ...
Added: October 14, 2018
А. В. Окунев, И. С. Шилин, Труды Математического института им. В.А. Стеклова РАН 2017 Т. 297 С. 260–280
Исследуются статистические аттракторы и аттракторы Милнора ступенчатых косых произведений над сдвигом Бернулли. В случае, когда слой – окружность, доказывается, что для топологически типичного косого произведения статистический аттрактор и аттрактор Милнора совпадают и являются устойчивыми по Ляпунову. Для этого рассматриваются некоторые свойства проекции аттрактора на слой, которые могут быть интересны сами по себе. В случае, когда слой – отрезок, дается ...
Added: October 14, 2018
Ivan Shilin, Moscow Mathematical Journal 2017 Vol. 17 No. 3 P. 511–553
We prove that for every smooth compact manifold M and any r>=1, whenever there is an open domain in Diff^r (M) exhibiting a persistent homoclinic tangency related to a basic set with a sectionally dissipative periodic saddle, topologically generic diffeomorphisms in this domain have Lyapunov unstable Milnor attractors. This implies, in particular, that the instability ...
Added: October 14, 2018
Yablonskii S. V., Kurbatov N. M., Parfenyev V.M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2017 Vol. 95 No. 1 P. 012707-1–012707-5
We study horizontal streaming excited by means of a low-frequency and low-intensity acoustic wave in 2D freely suspended films of thermotropic smectic liquid crystals. Acoustic pressure induces fast periodic transverse oscillations of the film, which produce in-plane stationary couples of vortices slowly rotating in opposite directions owing to hydrodynamic nonlinearity. The parameters of the vortices ...
Added: October 30, 2017
Gaydukov R. K., Borisov D. I., Mathematical notes 2016 Vol. 99 No. 5 P. 636–642
A fluid flow along a semi-infinite plate with small periodic irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure: a thin boundary layer (“lower deck”) and a classical Prandtl boundary layer (“upper deck”). The aim of this paper is to prove the existence and uniqueness of the ...
Added: May 18, 2016
Danilov V., Gaydukov R., Mathematical notes 2015 Vol. 98 No. 4 P. 561–571
We consider the problem of a viscous incompressible fluid flow along a flat plate with a small solitary perturbation (of hump, step, or corner type) for large Reynolds numbers. We obtain an asymptotic solution in which the boundary layer has a double-deck structure. ...
Added: September 27, 2015
Danilov V., Gaydukov R., Russian Journal of Mathematical Physics 2015 Vol. 22 No. 2 P. 161–173
A fluid flow along a plate with small irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure, i.e., both a thin boundary layer and the classical Prandtl boundary layer are present. It is proved that the solution of the boundary-value problem thus obtained exists and is unique ...
Added: September 3, 2015
Myshkis P. A., Международный журнал по теоретической и прикладной математике, классической и небесной механике, космодинамике 2013 № 2(3) С. 51–59
In the work received the necessary and sufficient condition for the existence for linear differential equation of n-th order the fundamental system of solutions expanding in Taylor series on multiple degrees of argument in the neighborhood of zero. Such condition is that coefficients of the equation have analogous decomposition. In the proof used the transition ...
Added: February 18, 2014