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Regular and Chaotic Oscillations in a Geostrophic Flow with Vertical Shear

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Abstract

The stability of flow with a constant vertical shear is investigated as part of a two-level quasi-geostrophic model. Analytical expressions for the increment of perturbation growth in linear stability theory are obtained. The Galerkin method with three basic Fourier harmonics is used to describe the nonlinear dynamics of perturbations. A nonlinear system of ordinary differential equations is formulated for amplitudes of Fourier harmonics. It is shown that, in the absence of bottom friction, all solutions of the system describe a periodic mode of nonlinear oscillations or vascillations. The situation changes fundamentally in the model with bottom friction. In this case, for a wide range of parameter values, the system solutions exhibit complex chaotic behavior. Thus, chaos or turbulence emerges for large-scale motions.

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ACKNOWLEDGMENTS

We thank M.V. Kurgansky and K.N. Visheratin for useful consultations and discussions of the results.

Funding

This work was supported by the Russian Science Foundation, project no. 23-17-00273 “Vortex and Wave Dynamics of the Changing Earth’s Atmosphere.”

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Authors and Affiliations

  1. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 109017, Moscow, Russia

    M. V. Kalashnik & O. G. Chkhetiani

  2. Schmidt Institute of Physics of the Earth, 123242, Moscow, Russia

    M. V. Kalashnik

  3. Research and Production Association Typhoon, 249038, Obninsk, Kaluga oblast, Russia

    M. V. Kalashnik

Authors
  1. M. V. Kalashnik
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  2. O. G. Chkhetiani
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Correspondence to M. V. Kalashnik.

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Kalashnik, M.V., Chkhetiani, O.G. Regular and Chaotic Oscillations in a Geostrophic Flow with Vertical Shear. Izv. Atmos. Ocean. Phys. 59, 489–497 (2023). https://doi.org/10.1134/S0001433823050067

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  • DOI: https://doi.org/10.1134/S0001433823050067

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