Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-17T02:28:14.514Z Has data issue: false hasContentIssue false
  • English
  • Français

Randomly forced Rayleigh-Bénard convection

Published online by Cambridge University Press:  19 April 2006

Bharat Jhaveri  and
G. M. Homsy
Bharat Jhaveri
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
G. M. Homsy
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the onset of Rayleigh–Bénard convection from random fluctuations arising within a fluid. In the specific case in which the fluctuations are thermodynamically determined, we reduce the problem to a random initial value problem for the Fourier modes. For the case of weak nonlinear convection, it is possible to truncate the number of modes and this truncated set is solved both by a Monte Carlo technique and by moment methods for various Rayleigh numbers. We find three stages in the evolution of ordered convection from random fluctuations which correspond to time intervals in which the fluctuations and the nonlinearity have different degrees of importance. It is shown that no simple moment truncation method will succeed and that the time for onset of convection is a mean over a distribution of times for which members of an ensemble exhibit appreciable convective transport.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 2 , 29 May 1980 , pp. 329 - 348
Copyright
© 1980 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

Ahlers, G. & Behringer, R. P. 1978 Phys. Rev. Lett. 40, 712.
Busse, F. H. & Clever, R. M. 1978 Bull. Am. Phys. Soc. 23 (8), 993.
Busse, F. H. & Clever, R. M. 1979 J. Fluid Mech. 91, 319.
Busse, F. H. & Whitehead, J. A. 1974 J. Fluid Mech. 66, 67.
Chandrasekhar, S. 1943 Rev. Mod. Phys. 19, 1.
Clever, R. M. & Busse, F. H. 1978 J. Appl. Math. Phys. 29, 711.
Coddington, E. A. & Levinson, N. 1955 Theory of Ordinary Differential Equations. McGraw Hill.
Davis, S. H. 1976 Ann. Rev. Fluid Mech. 8, 57.
Finucane, R. G. & Kelly, R. E. 1976 Int. J. Heat Mass Transfer 19, 71.
Fox, R. F. & Uhlenbeck, G. E. 1970 Phys. Fluids 13, 1893.
Graham, R. 1974 Phys. Rev. A 10, 1762.
Graham, R. & Pleiner, H. 1975 Phys. Fluids 18, 130.
Gresho, P. M. & Sani, R. L. 1971 Int. J. Heat Mass Transfer 14, 207.
Homsy, G. M. 1973 J. Fluid Mech. 60, 129.
Horne, R. N. 1979 J. Fluid Mech. 92, 751.
Keizer, J. 1978 Phys. Fluids 21, 198.
Knuth, D. 1969 The Art of Computer Programming, vol. 2. Englewood Cliffs, New Jersey: Addison-Wesley.
Landau, L. D. & Lifshitz, F. M. 1959 Fluid Mechanics. Pergamon Press.
Ludwig, D. 1975 SIAM Rev. 17, 605.
Malkus, W. & Veronis, G. 1958 J. Fluid Mech. 4, 225.
Newell, A. C., Lange, C. G. & Aucoin, P. J. 1970 J. Fluid Mech. 40, 543.
Schlüter, A., Lortz, D. & Busse, F. H. 1965 J. Fluid Mech. 23, 129.
Soong, P. T. 1973 Random Differential Equations in Science and Engineering. Academic Press.
Straus, J. M. & Schubert, G. 1979 J. Fluid Mech. 91, 155.
Suzuki, M. 1978 Proc. Ohji Symp., Tokyo, July 10–14.
Zaitsev, V. & Shliomis, M. 1971 Sov. Phys., J. Exp. Theor. Phys. 32, 866.