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Instability of unsteady flows or configurations. Part 2. Convective instability

Published online by Cambridge University Press:  29 March 2006

Chia-Shun Yih  and
Chin-Hsiu Li
Chia-Shun Yih
Affiliation:
Department of Engineering Mechanics, The University of Michigan
Chin-Hsiu Li
Affiliation:
Division of Fluid, Thermal and Aerospace Sciences, Case Western Reserve University, Cleveland
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Abstract

The formation of convective cells in a fluid between two horizontal rigid boundaries with time-periodic temperature distribution is studied by the use of the Floquet theory. Numerical results for the critical Rayleigh number are given for a Prandtl number of 0·73 (air) and for various values of the frequency and magnitude of the primary temperature oscillation. Some numerical results for a Prandtl number of 7·0 (water) are also given. The most striking feature of the results is that the disturbances (or convection cells) oscillate either synchronously or with half frequency.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 1 , 11 July 1972 , pp. 143 - 152
Copyright
© 1972 Cambridge University Press

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References

Benjamin, T. B. & Ursell, F. 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. Roy. Soc A 225, 505–515.Google Scholar
Chandrasekhar, S. 1954 The stability of viscous flow between rotating cylinders Mathematika, 1, 5–13.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Coddington, E. A. & Levinson, N. 1955 Theory of Ordinary Differential Equations, pp. 78–81. McGraw-Hill.
Donnelly, R. J. 1964 Experiments on the stability of viscous flow between rotating cylinders. III. Enhancement of stability by modulation. Proc. Roy. Soc A 281, 130–139.Google Scholar
Gresho, P. M. & Sani, R. L. 1970 The effects of gravity modulation on the stability of a heated layer J. Fluid Mech. 40, 783–806.Google Scholar
Ince, E. L. 1944 Ordinary Differential Equations. Dover.
Pellew, A. & Southwell, R. V. 1940 On maintained convective motion in a fluid heated from below. Proc. Roy. Soc A 176, 312–343.Google Scholar
Rosenblat, S. 1968 Centrifugal instability of time-dependent flows. Part 1. Inviscid periodic flows J. Fluid Mech. 33, 321–336.Google Scholar
Rosenblat, S. & Herbert, D. M. 1970 Low-frequency modulation of thermal instability J. Fluid Mech. 43, 385–398.Google Scholar
Rosenblat, S. & Tanaka, G. A. 1971 Modulation of thermal convection instability Phys. Fluids, 14, 1319–1322.Google Scholar
Venezian, G. 1969 Effect of modulation on the onset of thermal convection J. Fluid Mech. 35, 243–254.Google Scholar
Yih, C.-S. 1968 Instability of unsteady flows or configurations, Part 1. Instability of a horizontal liquid layer on an oscillating plane J. Fluid Mech. 31, 737–752.Google Scholar