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A numerical study of the occurrence of convection in a liquid layer under the influence of periodic external forces

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Abstract

The development of convection in a horizontal liquid layer located in a periodically modulated gravitational field (or with periodically varying temperature gradient) is examined. The effect of modulation frequency on stability is studied. Modulation stabilizes equilibrium if the direction of the gravitational force remains constant at all times. In the opposite case, stabilization occurs only at sufficiently high frequencies. In [1] the dependence of the critical Rayleigh number on modulation amplitude of the external force for several fixed frequencies was examined. In all cases examined in [1], the modulation proves to have a stabilizing influence.

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Literature Cited

  1. G. Z. Gershuni, E. M. Zhukhovitskii, and Yu. S. Yurkov, “Convective stability in the presence of a periodically varying parameter,” PMM,34, No. 3 (1970).

  2. G. S. Markman, “Equilibrium instability in a liquid under the influence of vibrational forces and a timeperiodic temperature gradient,” in: Mathematical Analysis and Its Application [in Russian], Vol. 2, Izd. Rostovsk. Un-ta (1970).

  3. L. D. Meshalkin and Ya. G. Sinai, “A study of the stability of the stationary state of one system of equations of planar motion of an incompressible viscous liquid,” PMM,25, No. 6 (1961).

  4. V. I. Yudovich, “An example of the development of secondary stationary or periodic flow with loss of stability in laminar flow of a viscous incompressible liquid,” PMM,29, No. 3 (1965).

  5. N. N. Moiseev, Asymptotic Methods in Nonlinear Mechanics [in Russian], Nauka, Moscow (1969).

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  6. S. Rosenblat and D. M. Herbert, “Low frequency modulation of thermal instability,” J. Fluid Mech.,43, No. 2 (1970).

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Authors
  1. G. S. Markman
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  2. V. I. Yudovich
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Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 81–86, May–June, 1972.

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Markman, G.S., Yudovich, V.I. A numerical study of the occurrence of convection in a liquid layer under the influence of periodic external forces. Fluid Dyn 7, 434–438 (1972). https://doi.org/10.1007/BF01209048

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  • DOI: https://doi.org/10.1007/BF01209048

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