Hostname: page-component-7bb8b95d7b-s9k8s Total loading time: 0 Render date: 2024-09-06T06:06:38.609Z Has data issue: false hasContentIssue false

Low-frequency modulation of thermal instability

Published online by Cambridge University Press:  29 March 2006

S. Rosenblat
Affiliation:
Mathematics Department, Imperial College, London
D. M. Herbert
Affiliation:
Mathematics Department, Imperial College, London

Abstract

A Boussinesq fluid is heated from below. The applied temperature gradient is the sum of a steady component and a low-frequency sinusoidal component. An asymptotic solution is obtained which describes the behaviour of infinitesimal disturbances to this configuration. The solution is discussed from the viewpoint of the stability or otherwise of the basic state, and possible stability criteria are analyzed. Some comparison is made with known experimental results.

Type
Research Article
Copyright
© 1970 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.)

References

Byrd, P. F. & Friedman, M. D. 1954 Handbook of Elliptic Integrals. Berlin: Springer.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Conrad, P. W. & Criminale, W. O. 1965 Z. angew. Math. Phys. 16, 23.
Donnelly, R. J. 1964 Proc. Roy. Soc. A 281, 130.
Gershuni, G. Z. & Zhukhovitskii, E. M. 1963 J. Appl. Math. Mech. 27, 119.
Rosenblat, S. 1968 J. Fluid Mech. 33, 32.
Venezian, G. 1969 J. Fluid Mech. 35, 24.