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Poincare Waves and Rossby Waves in Compressible Shallow Water Flows

  • STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
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Abstract

The shallow water approximation is generalized for describing large-scale flow of a liquid in the gravity field with a free surface. The classical shallow water equations are an alternative to the solution of the complete system of hydrodynamics equations in the gravity force field; however, the classical approximation does not take into account the density nonuniformity of a liquid layer. We have analyzed the flow of a thin layer of a rotating liquid with a free surface with account for the compressibility effects. We have obtained a system of quasi-linear differential equations describing the flow of a compressible liquid in the shallow water approximation. The solutions to this system have been obtained in the form of linear Poincare waves on the f plane and the Rossby waves on the β plane in compressed flows. The nonlinear dynamics of the Rossby waves in compressible flows is analyzed using the method of multiscale expansions. The resulting three-wave equations for the amplitudes of interacting waves are analyzed for parametric instabilities, and their increments are determined.

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Funding

This research was supported by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (grant no. 20-1-1-10).

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudny, Moscow oblast, Russia

    M. A. Yudenkova & A. S. Petrosyan

  2. Space Research Institute, Russian Academy of Sciences, 117997, Moscow, Russia

    M. A. Yudenkova, D. A. Klimachkov & A. S. Petrosyan

Authors
  1. M. A. Yudenkova
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  2. D. A. Klimachkov
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  3. A. S. Petrosyan
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Corresponding author

Correspondence to M. A. Yudenkova.

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The authors declare that there is no conflicts of interests.

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Translated by N. Wadhwa

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Yudenkova, M.A., Klimachkov, D.A. & Petrosyan, A.S. Poincare Waves and Rossby Waves in Compressible Shallow Water Flows. J. Exp. Theor. Phys. 134, 327–339 (2022). https://doi.org/10.1134/S1063776122020091

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  • DOI: https://doi.org/10.1134/S1063776122020091

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