Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-17T09:16:55.715Z Has data issue: false hasContentIssue false
  • English
  • Français

The dynamics and structure of double-diffusive layers in sidewall-heating experiments

Published online by Cambridge University Press:  21 April 2006

J. Tanny  and
A. B. Tsinober
J. Tanny
Affiliation:
Center for Technological Education, Holon, P.O. Box 305, Holon, Israel
A. B. Tsinober
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel-Aviv University, Tel-Aviv, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics and structure of double-diffusive layers were studied experimentally by heating a linear stable solute gradient from a sidewall in a wide tank. The formation and subsequent development of the layers were investigated by various flow-visualization techniques, namely fluorescent dye, fluorescent particles and shadowgraph. Experiments were performed in order to determine the stability diagram of the flow, following in each experiment the phase trajectory of the system in the phase plane of thermal and solute Rayleigh numbers. The experimentally obtained stability diagram appears to be similar to that obtained numerically by Thangam et al. (1981) and by Hart (1971) for a vertical narrow slot and a steady basic flow. It is shown that if the temperature of the sidewall rises slowly to its prescribed value, the thickness of the initial layers, formed at the onset of instability, is a function of the ambient density gradient and fluid properties only. On the other hand, if the wall temperature rises quickly (almost impulsive heating), the thickness of the initial layers is proportional to the imposed temperature difference, provided that the Rayleigh number, based on this difference, is larger than some critical value which is associated with the first merging of the layers. A criterion for the first merging of the initial layers is obtained, and it is suggested that this merging is due to subsequent instability of the system. The subsequent merging process, following the first merging, is not a simple successive doubling of the layer thickness and in each of five nearly identical experiments a different dependence of the average layer thickness on the instantaneous Rayleigh number is obtained. This indicates that the system of layers behaves chaotically after the first merging. The final thickness of the layers depends on the prescribed lateral temperature difference, and the ratio between the final and the initial thickness of the layers is a linear function of the final Rayleigh number. Flow-visualization experiments indicate that the layers consist of vortices with vertical scale of the layer thickness and various horizontal scales.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 196 , November 1988 , pp. 135 - 156
Copyright
© 1988 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

Chen, C. F., Briggs, D. G. & Wirtz, R. A. 1971 Stability of thermal convection in a salinity gradient due to lateral heating. Intl J. Heat Mass Transfer 14, 57–65.Google Scholar
Hart, J. E. 1971 On sideways diffusive instability. J. Fluid Mech. 49, 279–288.Google Scholar
Hart, J. E. 1973 Finite amplitude sideways diffusive convection. J. Fluid Mech. 59, 47–64.Google Scholar
Huppert, H. E., Kerr, R. C. & Hallworth, M. A. 1984 Heating or cooling a stable compositional gradient from the side. Intl J. Heat Mass Transfer 27, 1395–1401.Google Scholar
Huppert, H. E. & Linden, P. F. 1979 On heating a stable salinity gradient from below. J. Fluid Mech. 95, 431–464.Google Scholar
Huppert, H. E. & Turner, J. S. 1980 Ice blocks melting into a salinity gradient. J. Fluid Mech. 100, 367–384.Google Scholar
Huppert, H. E. & Turner, J. S. 1981 Double-diffusive convection. J. Fluid Mech. 106, 299–329.Google Scholar
Linden, P. F. 1976 The formation and destruction of fine-structure by double diffusive process. Deep-Sea Res. 23, 895–908.Google Scholar
Narusawa, U. & Suzukawa, Y. 1981 Experimental study of double-diffusive cellular convection due to a uniform lateral heat flux. J. Fluid Mech. 113, 387–405.Google Scholar
Paliwal, R. C. & Chen, C. F. 1980 Double-diffusive instability in an inclined fluid layer. Part 2. Stability analysis. J. Fluid Mech. 98, 769–785.Google Scholar
Suzukawa, Y. & Narusawa, U. 1982 Structure of growing double diffusive convection cells. Trans. ASME C: J. Heat Transfer 104, 248–254Google Scholar
Tanny, J. & Tsinober, A. B. 1987 On the merging of double diffusive layers. In Proc. 3rd Intl Symp. on stratified flows, CIT, California.
Thangam, S., Zebib, A. & Chen, C. F. 1981 Transition from shear to sideways diffusive instability in a vertical slot. J. Fluid Mech. 112, 151–160.Google Scholar
Thorpe, S. A., Hutt, P. K. & Soulsby, R. 1969 The effect of horizontal gradients on thermohaline convection. J. Fluid Mech. 38, 375–400.Google Scholar
Tsinober, A. B. & Tanny, J. 1985 On the structure and dynamics of double diffusive layers in sidewall heating experiments. In Double Diffusive Motions (ed. N. E. Bixler & E. Speigel), FED-vol. 24, pp. 39–45. ASME.
Tsinober, A. B. & Tanny, J. 1986 Visualization of double diffusive layers. In Flow Visualization IV (ed. Claude Veret), pp. 345–351. Hemisphere.
Tsinober, A. B., Yahalom, Y. & Shlien, D. J. 1983 A point source of heat in a stable salinity gradient. J. Fluid Mech. 135, 199–217.Google Scholar
Turner, J. S. 1974 Double diffusive phenomena. A. Rev. Fluid Mech. 6, 37–56.Google Scholar
Turner, J. S. 1978 Double-diffusive intrusion into a density gradient. J. Geophys. Res. 83, 2887–2901.Google Scholar
Turner, J. S. 1979 Laboratory models of double diffusive processes in ocean. In Proc. 12th Symp. Naval Hydr., Washington D.C., pp. 596–606.
Turner, J. S. 1985 Multicomponent convection. Ann. Rev. Fluid Mech. 17, 11–44.Google Scholar
Turner, J. S. & Chen, C. F. 1974 Two dimensional effects in double diffusive convection. J. Fluid Mech. 63, 577–592.Google Scholar
Wirtz, R. A., Briggs, D. G. & Chen, C. F. 1972 Physical and numerical experiments on layered convection in a density-stratified fluid. Geophys. Fluid Dyn. 3, 265–288.Google Scholar
Wirtz, R. A. & Reddy, C. S. 1979 Experiments on convective layer formation and merging in a differentially heated slot. J. Fluid Mech. 91, 451–464.Google Scholar