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TEMPERATURE MODULATION IN RAYLEIGH–BÉNARD CONVECTION

Part of:Incompressible viscous fluids

Published online by Cambridge University Press:  01 October 2008

JITENDER SINGH and
RENU BAJAJ
JITENDER SINGH*
Affiliation:
Indian Statistical Institute, Kolkata-700108, India (email: jitender_r@isical.ac.in)
RENU BAJAJ
Affiliation:
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh-160014, India (email: rbajaj@pu.ac.in)
*
✉For correspondence; e-mail: jitender_r@isical.ac.in
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Abstract

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The stability characteristics of an infinite horizontal fluid layer excited by a time-periodic, sinusoidally varying free-boundary temperature, have been investigated numerically using the Floquet theory. It has been found that the modulation of the temperature gradient across the fluid layer affects the onset of the Rayleigh–Bénard convection. Modulation can give rise to instability in the subcritical conditions and it can also suppress the instability in the supercritical cases. The instability in the fluid layer manifests itself in the form of either a harmonic or subharmonic flow, controlled by thermal modulation.

Keywords

convectiontemperature modulationparametric instability

MSC classification

Secondary:76D17: Viscous vortex flows

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 2 , October 2008, pp. 231 - 245
Copyright
Copyright © Australian Mathematical Society 2009

References

[1]Bajaj, R., “Thermo-magnetic convection in ferrofluids with gravity-modulation”, Indian J. Eng. Mater. Sci. 10 (2002) 282–291.Google Scholar
[2]Bodenschatz, E., Pesch, W. and Ahler, G., “Recent developements in Rayleigh–Bénard convection”, Annu. Rev. Fluid Mech. 32 (2000) 709–778.CrossRefGoogle Scholar
[3]Chandrasekhar, S., Hydrodynamic and hydromagnetic stability (Oxford University Press, Oxford, 1966).Google Scholar
[4]Chen, W. Y. and Chen, C. F., “Effect of gravity modulation on the stability of convection in a vertical slot”, J. Fluid Mech. 395 (1999) 327–344.CrossRefGoogle Scholar
[5]Drazin, P. and Reid, W., Hydrodynamic stability (Cambridge University Press, Cambridge, 1981).Google Scholar
[6]Farkas, M., Periodic motions (Springer-Verlag, New York, 1994).CrossRefGoogle Scholar
[7]Gresho, P. M. and Sani, R. L., “The effect of gravity modulation on the stability of a heated fluid layer”, J. Fluid Mech. 40 (1970) 783.CrossRefGoogle Scholar
[8]Jordan, D. W. and Smith, P., Nonlinear ordinary differential equations (Clarendon Press, Oxford, 1988).Google Scholar
[9]Koschmieder, E. L., Bénard cells and Taylor vortices (Cambridge University Press, Cambridge, 1993).Google Scholar
[10]Kumar, K., “Linear theory of Faraday instability in viscous liquids”, Proc. R. Soc. Lond. A 452 (1994) 1113–1126.Google Scholar
[11]Nelson, E., Topics in dynamics I: flows (Princeton University Press and University of Tokyo Press, Princeton, NJ, 1969).Google Scholar
[12]Roppo, M. N., Davis, S. H. and Rosenblat, S., “Bénard convection with time-periodic heating”, Phys. Fluids 27 (1984) 796–803.CrossRefGoogle Scholar
[13]Rosenblat, S. and Tanaka, G. A., “Modulation of thermal convection instability”, Phys. Fluids 14 (1971) 1319–1322.CrossRefGoogle Scholar
[14]Venezian, G., “Effect of modulation on the onset of thermal convection”, J. Fluid Mech. 395 (1999) 327–344.Google Scholar
[15]Yih, C. S. and Li, C. H., “Instability of unsteady flows or configurations. Part 2. Convective instability”, J. Fluid Mech. 54 (1972) 143–152.CrossRefGoogle Scholar