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Mixed mode convection in an inclined slot

Published online by Cambridge University Press:  26 April 2006

K. Fujimura  and
R. E. Kelly
K. Fujimura
Affiliation:
Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319–11, Japan
R. E. Kelly
Affiliation:
Mechanical, Aerospace and Nuclear Engineering Department, University of California, Los Angeles, CA 90024–1597, USA
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Abstract

Nonlinear interaction between transverse disturbances and longitudinal rolls has been investigated for flow in an inclined slot with a heated lower wall when both modes of instability occur at nearly the same value of the control parameter. This condition is shown to be possible for a fluid with Prandtl number greater than 0.263 897, For slightly supercritical values of the Rayleigh number (R) when the critical Rayleigh number for longitudinal rolls RLC is somewhat less than that for transverse stationary rolls, RSC, and for transverse travelling waves, RTC, longitudinal rolls occur first and then remain stable as R is increased beyond RSC or RTC; no mixed mode state occurs. In contrast, if RSc or RTc is slightly below RLC, pure transverse modes exist for only a relatively small range of R beyond RSC or RTC. Thereafter, a three-dimensional mixed mode state occurs well before RLC is reached, i.e. three-dimensionality sets in on a subcritical basis. As R approaches RLC the contribution of the transverse mode decreases continuously until a pure longitudinal roll state emerges for R slightly greater than RLC. Mixed mode convection is also investigated for a special choice of parameters when three modes, namely transverse stationary rolls, transverse travelling waves and longitudinal rolls, become unstable simultaneously. Longitudinal rolls again emerge as the stable supercritical state.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 246 , January 1993 , pp. 545 - 568
Copyright
© 1993 Cambridge University Press

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References

Bergholz, R. F. 1978 J. Fluid Mech. 84, 743– 768.
Brand, H. R., Deissler, R. J. & Ahlers, G. 1991 Phys. Rev. A 43, 4262– 4268.
Busse, F. H. & Clever, R. M. 1992 J. Engng Maths 26, 1– 20.
Chen, M. M. & Whitehead, J. A. 1968 J. Fluid Mech. 31, 1– 15.
Chen, Y.-M. & Pearlstein, A. J. 1989 J. Fluid Mech. 198, 513– 541.
Clever, R. M. & Busse, F. H. 1977 J. Fluid Mech. 81, 107– 127.
Fujimura, K. 1992 Eur. J. Mech. B/Fluids 11, 461– 464.
Fujimura, K. & Mizushima, J. 1991 Eur. J. Mech. B/Fluids 10, Suppl. No. 2, 26– 30.
Gershuni, G. Z. & Zhukhovitskii, E. M. 1969 Prikl. Mat. Mech. 33, 855– 860.
Hart, J. E. 1971 J. Fluid Mech. 47, 547– 576.
Hollands, K. G. T. & Konicek, L. 1973 Intl J. Heat Mass Transfer 16, 1467– 1476.
Kirchartz, K. R. & Oertel, H. 1988 J. Fluid Mech. 192, 249– 286.
Korpela, S. A. 1974 Intl J. Heat Mass Transfer 17, 215– 222.
Kropf, M. & Busse, F. H. 1991a Phys. Fluids A 3, 2988– 2994.
Kropp, M. & Busse, F. H. 1991b In Bifurcation and Chaos (ed. T. Küpper, R. Seydel & F W. Schneider), pp. 217– 223. Birkliäuser.
Luijkx, L. M., Flatten, J. K. & Legros, J. C. 1981 Intl J. Heat Mass Transfer 24, 1287– 1292.
Müller, H. W., Lücke, M. & Kamps, M. 1989 Europhys. Lett. 10, 451– 456.
Müller, H. W., Lücre, M. & Kamps, M. 1992 Phys. Rev. A 45, 3714– 3726.
Ouazzani, M. T., Platten, J. K. & Mojtabi, A. 1990 Intl J. Heat Mass Transfer 33, 1417– 1427.
Platten, J. K. & Legros, J. C. 1984 Convection in Liquids. Springer.
Richter, F. M. 1973 J. Geophys. Res. 78, 8735– 8745.
Richter, F. M. & Parsons, B. 1975 J. Geophys. Res. 80, 2529– 2541.
Rosenblat, S. 1982 J. Fluid Mech. 122, 395– 410.
Shadid, J. N. & Goldstein, R. J. 1990 J. Fluid Mech. 215, 61– 84.