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Nonlinear Marangoni convection in bounded layers. Part 2. Rectangular cylindrical containers

Published online by Cambridge University Press:  20 April 2006

S. Rosenblat ,
G. M. Homsy  and
S. H. Davis
S. Rosenblat
Affiliation:
SHD Associates, Inc., 2735 Simpson St, Evanston, IL 60201, U.S.A.
G. M. Homsy
Affiliation:
SHD Associates, Inc., 2735 Simpson St, Evanston, IL 60201, U.S.A.
S. H. Davis
Affiliation:
SHD Associates, Inc., 2735 Simpson St, Evanston, IL 60201, U.S.A.
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Abstract

Attention is confined to roll-cell development and roll-cell interaction appropriate to one horizontal dimension larger than either the other horizontal dimension or the depth. At simple eigenvalues Mc the roll-cell amplitude and transport fields can be obtained. Near those aspect ratios corresponding to double eigenvalues Mc, where two roll-cell states of linear theory areequallylikely, thenonlinear theory predicts sequences of transitions from one steady convective state to another as the Marangoni number is increased. Direct comparisons are made of the results here with those of the previous paper for Marangoni convection in circular cylinders. Time-periodic convection is possible in certain cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 120 , July 1982 , pp. 123 - 138
Copyright
© 1982 Cambridge University Press

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References

Beck, J. L. 1972 Phys. Fluids 15, 1377.
Davis, S. H. 1967 J. Fluid Mech. 30, 465.
Pearson, J. R. A. 1958 J. Fluid Mech. 4, 489.
Rosenblat, S. 1979 Stud. Appl. Math. 60, 241.
Rosenblat, S. 1982 Pending publication.
Rosenblat, S., Davis, S. H. & Homsy, G. M. 1982 J. Fluid Mech. 120, 91.
Scanlon, J. W. & Segel, L. A. 1967 J. Fluid Mech. 30, 149.