Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-09T22:50:47.406Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite amplitude sideways diffusive convection

Published online by Cambridge University Press:  29 March 2006

J. E. Hart
J. E. Hart
Affiliation:
Department of Astro-Geophysics, University of Colorado, Boulder
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the flow in a differentially heated vertical slot filled with a stably stratified solution. The stability of the flow driven by the differential heating is investigated in the limits of small but finite amplitude disturbances and very large solute Rayleigh number RS = gβ(∂Sa/∂z)D4/KSv. If the Schmidt number H = KT/KS is of order 1, the growth of an initial perturbation at the neutral point is balanced by horizontal advection of solute and heat, and a steady equilibration amplitude is attained. The Nusselt number is independent of all fluid properties and is directly proportional to the Rayleigh number excess ε = (Ra – Rac)/Rac. If H is much greater than |RS|⅙, or if the disturbance wave-number is slightly less than the critical wavenumber, subcritical instabilities are possible. In particular a resonant instability is possible. These theoretical predictions are consistent with previous experimental results and with the laboratory results described in this paper. In the experiments we find that the mixing of the initial sugar gradient is accomplished by convection cells which undergo transitions to larger wavelengths. The breakdown of the interfaces between convection cells is described.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 1 , 5 June 1973 , pp. 47 - 64
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.)

References

Baines, P. G. & Gill, A. E. 1969 On thermohaline convection with linear gradients J. Fluid Mech. 37, 289.Google Scholar
Baker, D. J. 1966 A technique for the precise measurement of small fluid velocities J. Fluid Mech. 26, 273.Google Scholar
Baker, D. J. 1971 Density gradients in a rotating stratified fluid: experimental evidence for a new instability. Science, 172, 1029.Google Scholar
Blumsack, S. L. 1967 Formation of layers in a stably stratified fluid. Geophys. Fluid Dyn. Summer Notes II, W.H.O., p. 1.Google Scholar
Chen, C. F., Briggs, D. & Wirtz, R. A. 1971 Stability of thermal convection in a salinity gradient due to lateral heating Int. J. Heat & Mass Transfer, 14, 57.Google Scholar
Hart, J. E. 1971 On sideways diffusive instability J. Fluid Mech. 49, 279.Google Scholar
Mcintyre, M. E. 1970 Diffusive destabilization of the baroclinic circular vortex Geophys. Fluid Dyn. 1, 19.Google Scholar
Nikolaev, B. I. & Tubin, A. P. 1971 On the stability of convective motions of a binary mixture in a plane thermal diffusion column Prikl. Math. Mech. 35, 248.Google Scholar
Oster, G. 1965 Density gradients Sci. Amer. 213, 70.Google Scholar
Raetz, G. S. 1959 Northrop Rep. NOR-59-383 BLC-121. (See Stuart 1962.)
Stern, M. E. 1960 The salt fountain and thermohaline convection Tellus, 12, 172.Google Scholar
Stuart, J. T. 1962 Nonlinear effects in hydrodynamic stability. Proc. 10th Int. Congr. Appl. Mech. p. 63. Elsevier.
Thorpe, S. A., Hutt, P. K. & Soulsby, R. 1969 The effect of horizontal gradients on thermohaline convection J. Fluid Mech. 38, 375.Google Scholar
Turner, J. S. 1968 The behaviour of a stable salinity gradient heated from below J. Fluid Mech. 33, 183.Google Scholar
Turner, J. S. & Stommel, H. 1964 A new case of convection in the presence of combined vertical salinity and temperature gradients Proc. U.S. Nat. Acad. Sci. 52, 49.Google Scholar
Veronis, G. 1965 On finite amplitude instability in thermohaline convection. J. Mar. Res. 23, 7.Google Scholar
Veronis, G. 1968 Effects of a stabilizing gradient of solute on thermal convection J. Fluid Mech. 34, 315.Google Scholar
Wirtz, R. A., Briggs, D. & Chen, C. F. 1972 Physical and numerical experiments on layered convection in a density-stratified fluid Geophys. Fluid Dyn. 3, 265.Google Scholar