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The formation of layers in a double-diffusive system with a sloping boundary

Published online by Cambridge University Press:  12 April 2006

P. F. Linden  and
J. E. Weber
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
J. E. Weber
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Present address: Institute of Mathematics, Mechanics Department, University of Oslo.
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Abstract

The flows induced by the presence of an insulating sloping boundary in a doublediffusive system are examined. In the diffusive case, when the component with the larger diffusivity is unstably distributed, it is known that under certain circumstances horizontal motions are induced near the slope, and that a series of horizontal layers forms. We investigate the formation and properties of the layers, in particular their vertical scale and its dependence on the stratification and the slope angle. The scale of the layers is found to be a strong function of Gρ, the ratio of the vertical density gradient of the unstably distributed component to that of the stably distributed component. At low values of Gρ, no layering was observed; at larger values of Gρ layers were formed, and their scale increased as Gρ → 1. A weak dependence of scale on slope angle was also observed with the scale diminishing as the angle of the slope to the horizontal increased.

A new form of layering has been observed when the basic stratification is in the finger sense. At high enough values of Gρ the basic stratification is unstable to finger motions and these exist throughout the fluid. When a slope is introduced, horizontal motions are set up near the slope which cause the fingers to break down and layers are produced. There is considerable horizontal motion in these layers as well as convective motions driven by the fingers in the interfaces between the layers. The formation of these layers and some of their properties are documented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 4 , 5 August 1977 , pp. 757 - 773
Copyright
© 1977 Cambridge University Press

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References

Chen, C. F. 1975 Double-diffusive convection in an inclined slot. J. Fluid Mech. 72, 721–729.Google Scholar
Chen, C. F., Briggs, D. G. & Wirtz, R. A. 1971 Stability of thermal convection in a salinity gradient due to lateral heating. Int. J. Heat Mass Transfer 14, 57–66.Google Scholar
Chen, C. F. & Wong, S. B. 1974 Double-diffusive convection along a sloping wall. Bull. Am. Phys. Soc. 19, 1154.Google Scholar
Hart, J. E. 1971 On sideways diffusive instability. J. Fluid Mech. 49, 279–288.Google Scholar
Linden, P. F. 1976 The formation and destruction of fine-structure by double-diffusive processes. Deep-Sea Res. 23, 895–908.Google Scholar
Oster, G. 1965 Density gradients. Scient. Am. 213, 70–76.Google Scholar
Phillips, O. M. 1970 On flows induced by diffusion in a stably stratified fluid. Deep-Sea Res. 17, 435–443.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
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S. & Chen, C. F. 1974 Two-dimensional effects in double-diffusive convection. J. Fluid Mech. 63, 577–592.Google Scholar
Wunsch, C. 1970 On oceanic boundary mixing. Deep-Sea Res. 17, 293–301.Google Scholar