Hostname: page-component-7dd5485656-s6l46 Total loading time: 0 Render date: 2025-10-30T16:22:08.881Z Has data issue: false hasContentIssue false
  • English
  • Français

The stability of a periodically heated layer of fluid

Published online by Cambridge University Press:  20 April 2006

John Dowden
John Dowden
Affiliation:
Department of Mathematics, University of Essex, Colchester C04 3SQ, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of an infinite layer of fluid of uniform thickness at rest with two horizontal boundaries is investigated when the difference between the temperatures at the top and bottom boundaries has a component which is a fluctuating periodic function of time in addition to a constant part. When both boundaries are free small fluctuations have a stabilizing effect on the layer, while large fluctuations tend to make it less stable, consistently with the numerical results of Yih & Li (1972); the effect is attributable entirely to the variation of the temperature gradient with time. An approximate relation between the mean Rayleigh number and the amplitude of the fluctuations is found which separates stable situations from unstable ones. This is compared with the criteria deduced by Homsy (1974) using energy arguments for disturbances of any amplitude.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 110 , September 1981 , pp. 149 - 159
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Chandra, K. 1938 Instability of fluids heated from below. Proc. Roy. Soc. A 164, 231–242.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Currie, I. G. 1967 The effect of heating rate on the stability of stationary fluids. J. Fluid Mech. 29, 337–347.Google Scholar
Davis, S. H. 1976 The stability of time-periodic flows. Ann. Rev. Fluid Mech. 8, 57–74.Google Scholar
Goldstein, A. W. 1959 Stability of a horizontal fluid layer with unsteady heating from below and time-dependent body forces. N.A.S.A. Tech. Rep. no. R-4.Google Scholar
Graham, A. 1933 Shear patterns in an unstable layer of fluid. Phil. Trans. Roy. Soc. A 232, 285–296.Google Scholar
Gresho, P. M. & Sani, R. L. 1970 The effect of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech. 40, 783–806.Google Scholar
Homsy, G. M. 1974 Global stability of time-dependent flows. Part 2. Modulated fluid layers. J. Fluid Mech. 62, 387–404.Google Scholar
Jeffreys, H. 1924 On certain approximate solutions of linear differential equations of the second order. Proc. Lond. Math. Soc. 23, 428–436.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 convective instability. Phys. Fluids 14, 1319–1322.Google Scholar
Strutt, M. J. O. 1932 Lamésche-, Mathieusche- und verwandte Functionen in Physik und Technik. Ergebn. Math. 1, 199–323.Google Scholar
Strutt, M. J. O. 1943 Eigenwaarde-krommen bij problemen van Hill. II. Asymptotisch verloop der krommen. Versl. gewone Vergad. Afd. Natuurk. K. ned. Akad. Wet. 52, 212–222.Google Scholar
Sutton, O. G. 1950 On the stability of a fluid heated from below. Proc. Roy. Soc. A 204, 297–309.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. & Li, C.-H. 1972 Instability of unsteady flows or configurations. Part 2. Convective instability. J. Fluid Mech. 54, 143–152.Google Scholar