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The instability of a fluid layer with time-dependent heating

Published online by Cambridge University Press:  28 March 2006

Wilbert Lick
Wilbert Lick
Affiliation:
Harvard University
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Abstract

The problem of the stability and growth of disturbances in a fluid with time-dependent heating is investigated. The analysis is restricted to the case when the temperature gradient is large in a layer which is narrow by comparison with the overall depth of the fluid. An approximate method of solution is presented. Results of computations are also presented which illustrate the method of solution and the essential features of the problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 21 , Issue 3 , March 1965 , pp. 565 - 576
Copyright
© 1965 Cambridge University Press

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References

Bénard, H. 1900 Tourbillions cellulaires dans une nappe liquide. Rev. gen. Sci. pur. appl. 11, 1261–71, 1309–28.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Goldstein, A. W. 1959 Stability of a horizontal fluid layer with unsteady heating from below and time dependent body forces. NASA Tech. Rep. no. R-4.Google Scholar
Gribov, V. N. & Gurevich, L. E. 1957 On the theory of the stability of a layer located at superadiabatic temperature gradient in a gravitational field. Soviet Phys., JETP, 4, 720–9.Google Scholar
Jeffreys, H. 1926 The stability of a layer of fluid heated below. Phil. Mag. 2, 833–44.Google Scholar
Jeffreys, H. 1928 Some cases of instability in fluid motion. Proc. Roy. Soc. A, 118, 195–208.Google Scholar
Jeffreys, H. 1962 Asymptotic Approximations. Oxford University Press.
Low, A. R. 1929 On the criterion for stability of a layer of viscous fluid heated from below. Proc. Roy. Soc. A, 125, 180–95.Google Scholar
Morton, B. R. 1957 On the equilibrium of a stratified layer of fluid. Quart. J. Mech. Appl. Math. 10, 433–47.Google Scholar
Ostrach, S. 1957 Convection phenomena in fluids heated from below. Trans. A.S.M.E. 79, 299–305.Google Scholar
Pellew, A. R. & Southwell, R. V. 1940 On maintained convective motion in a fluid heated from below. Proc. Roy. Soc. A, 176, 312–43.Google Scholar
Rayleigh, Lord 1916 On convection currents in a horizontal layer of fluid when the higher temperature is on the underside. Phil. Mag. 32, 529–46.Google Scholar
Sparrow, E. M., Goldstein, R. J. & Jonsson, V. K. 1964 Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile. J. Fluid Mech. 18, 513–28.CrossRefGoogle Scholar
Stuart, J. T. 1964 On the cellular patterns in thermal convection. J. Fluid Mech. 18, 481–98.Google Scholar
Thomson, J. 1882 On a changing tessellated structure in certain fluids. Proc. Glasgow Phil. Soc. 13, 469.Google Scholar