Hostname: page-component-5b777bbd6c-gtgcz Total loading time: 0 Render date: 2025-06-20T20:53:56.658Z Has data issue: false hasContentIssue false
  • English
  • Français

Some further studies on the transition to turbulent convection

Published online by Cambridge University Press:  29 March 2006

Ruby Krishnamurti
Ruby Krishnamurti
Affiliation:
The Geophysical Fluid Dynamics Institute and The Department of Oceanography, Florida State University, Tallahassee
Get access Rights & Permissions [Opens in a new window]

Abstract

In a horizontal convecting layer of fluid, several distinct transitions occur at certain distinct Rayleigh numbers R, for a given Prandtl number Pr. The regime diagram has been extended to include the Prandtl-number range

2·5 × 10−2 [les ] Pr [les ] 0·85 × 104.

In particular it is found that distinct changes in the slope of the heat-flux curve occur even for Pr = 2·5 × 10−2. The flow is steady up to R = Rt = 2·4 × 103. For R > Rt, the period of oscillation is compared with the theoretical values of Busse. For Pr = 0·71 decreases as well as increases in the slope of the heat-flux curve are observed.

For R just greater than Rc, the preferred orientation of rolls in various side-wall geometries is investigated. For high Prandtl number, the effect of curvature of the roll axis, forced by curved side walls, upon the second transition at RII is investigated. It is found that curvature, as well as previously discussed effects, leads to a lowering of RII. These results, along with the observed hysteresis, support the view that there are metastable states attainable by finite amplitude instability. Finally the nature of the time-dependent flow at large R and high Prandtl number is investigated in a Hele-Shaw cell. It is shown unequivocally that the observed periodicity at a fixed point is due to hot or cold plumes moving past the point.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 60 , Issue 2 , 4 September 1973 , pp. 285 - 303
Copyright
© 1973 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

Benning, A. F. & Markwood, W. H. 1939 Refrig. Engng, 37, 243–47.
Busse, F. H. 1967 J. Fluid Mech. 30, 625.
Busse, F. H. 1968 J. Math. & Phys. 46, 140.
Busse, F. H. 1972 J. Fluid Mech. 52, 97.
Chen, M. M. & Whitehead, J. A. 1968 J. Fluid Mech. 31, 1.
Davis, S. H. 1967 J. Fluid Mech. 30, 465.
Elder, J. W. 1967 J. Fluid Mech. 27, 609.
Hele-Shaw, H. S. J. 1898 Trans. Inst. Nav. Arch. 40, 21.
Koschmieder, L. 1966 Beit. Z. Phys. Atmos. 39, 1.
Krishnamurti, R. 1967 Ph.D. dissertation, University of California, Los Angeles.
Krishnamurti, R. 1968a J. Fluid Mech. 33, 445.
Krishnamurti, R. 1968b J. Fluid Mech. 33, 457.
Krishnamurti, R. 1970a J. Fluid Mech. 42, 295.
Krishnamurti, R. 1970b J. Fluid Mech. 42, 309.
Lamb, H. 1932 Hydrodynamics. Dover.
Malkus, W. V. R. 1954 Proc. Roy. Soc. A, 225, 185.
Rossby, H. T. 1966 Ph.D. dissertation, Massachusetts Institute of Technology.
Schlüter, A., Lortz, D. & Busse, F. 1965 J. Fluid Mech. 23, 129.
Schneck, P. & Veronis, G. 1967 Phys. Fluids, 10, 924.
Segel, L. A. 1969 J. Fluid Mech. 38, 203.
Willis, G. E. & Deardorff, J. W. 1965 Phys. Fluids, 8, 2225.
Willis, G. E. & Deardorff, J. W. 1967a Phys. Fluids, 10, 931.
Willis, G. E. & Deardorff, J. W. 1967b Phys. Fluids, 10, 1861.
Willis, G. E. & Deardorff, J. W. 1970 J. Fluid Mech. 44, 661.