Abstract
The effect of vertical vibrations on the convection in a rotating planar fluid layer heated from below was studied. In this case a modulation parameter, the acceleration due to gravity, appears in the problem. The modulation of the parameter may have a significant effect on the onset of convective instability. Parameter modulation in nonrotating layers has been investigated in earlier work [1–3]. The presence of rotation significantly increases the complexity of the mathematical problem, introducing an additional dependence of the solution on the Taylor number Ta and the Prandtl number Pr. Furthermore, an oscillatory convection regime can occur at the stability limit in rotating fluids with Pr < 1. Parameter modulation in the rotating fluid may not only lead to a change in the stability limit and critical wavelength but also to a change in the eigenfrequency of the oscillatory convection. Rauscher and Kelly [4] examined the effect of parameter modulation on the convective stability of a rotating fluid only for the particular case of a sinusoidal variation in the temperature gradient with a small amplitude for Pr = 1, i.e., the effect of modulation was studied on only a steady convection regime.
Similar content being viewed by others
Literature cited
G. Z. Gershuni and E. M. Zhukovitskii, “Parametric excitation of convective instability,” Prikl. Mat. Mekh.,27, 779 (1963).
G. Z. Gershuni, E. M. Zhukhovitskii, and Yu. S. Yurkov, “Convective stability in the presence of a periodically varying parameter,” Prikl. Mat. Mekh.,34, 470 (1970).
G. Z. Gershuni, E. M. Zhukhovitskii, and Yu. S. Yurkov, “Numerical determination of the boundaries for convective instability in a system with periodically varying parameter,” in: Hydrodynamics, No. 3 [in Russian], Perm' (1971), pp. 29–37.
J. W. Rauscher and R. E. Kelly, “Effect of modulation on the onset of thermal convection in a rotating fluid,” Int. J. Heat Mass Transfer,18, 1216 (1975).
L. D. Landau and E. M. Lifshitz, Mechanics, 2nd ed., Pergamon Press, Oxford (1969).
N. N. Bogolyubov and Yu. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).
G. Z. Gershuni and E. M. Zhukhovitskii, Convective Instability of an Incompressible Fluid [in Russian], Nauka, Moscow (1972).
G. Venezian, “Effect of modulation on the onset of thermal convection,” J. Fluid Mech.,35, 243 (1969).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 12–22, July–August, 1984.
Rights and permissions
About this article
Cite this article
Bogoyavlenskii, A.B., Yavorskaya, I.M. The effect of vertical vibrations on the onset of convection in a planar rotating layer. Fluid Dyn 19, 523–531 (1984). https://doi.org/10.1007/BF01091071
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01091071