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Hydrodynamic Instability of Vertical Motions Excited by Spatially Periodic Distributions of Heat Sources

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Abstract–

The hydrodynamic instability of a system of vertical motions initiated by spatially periodic distributions of heat sources is investigated. The Galerkin method with three basis trigonometric functions is used to describe the perturbation dynamics. The nonlinear system of equations for finding the expansion coefficients is formulated. It is found that the vertical motions are unstable in the absence of dissipation if the Richardson number is less than one eighth. A weakly nonlinear model of inviscid instability is developed. It is shown that the loss of stability in the presence of dissipation can lead to formation of either steady-state or time-oscillating secondary flow with nontrivial streamline topology.

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Funding

The work was carried out with support from the Russian Foundation for Basis Research (projects nos. 18-05-00414a and 18-05-00831a).

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Authors and Affiliations

  1. Obukhov Institute of Atmospheric Physics of the Russian Academy of Sciences, 119017, Moscow, Russia

    M. V. Kalashnik & M. V. Kurgansky

  2. Scientific and Production Association ”Typhoon”, 249038, Obninsk, Russia

    M. V. Kalashnik

Authors
  1. M. V. Kalashnik
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  2. M. V. Kurgansky
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Corresponding authors

Correspondence to M. V. Kalashnik or M. V. Kurgansky.

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Translated by E.A. Pushkar

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Kalashnik, M.V., Kurgansky, M.V. Hydrodynamic Instability of Vertical Motions Excited by Spatially Periodic Distributions of Heat Sources. Fluid Dyn 55, 554–565 (2020). https://doi.org/10.1134/S0015462820040060

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  • DOI: https://doi.org/10.1134/S0015462820040060

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