J. Fluid Mech. (1979), vol. 95, part 3, pp. 431-464 Printed in Great Britain 43 1 On heating a stable salinity gradient from below By HERBERT E. HUPPERT AND P. F. LINDEN Department of Applied Mathematics and Theoretical Physics, University of Cambridge (Received 20 December 1978) When heat is applied at the bottom of a stable salinity gradient a series of layers with uniform temperature and salinity is formed. The evolution of this system is investigated in the laboratory and a numerical model of the process is developed. New layers are formed sequentially at the top of a growing convection region while lower down adjacent layers merge. For given fluid properties the convection depends upon one parameter Q, which is proportional to the (suitably non-dimensionalized) ratio of the salinity gradient to the heat flux. We find that the depth of the top of the convecting region and the number of layers present increase like the square root of time over the range of Q examined. This permits the definition of an effective conductivity, K,, for the total series of layers which is directly proportional to K ~ , the molecular thermal diffusivity, and inversely proportional to Q. The vertical growth of the layers is thus retarded by increasing Q. The average thickness of t'he layers decreases with increasing salinity gradient and appears to be independent of the applied heat flux. 1. Introduction Double-diffusive convection occurs in a fluid with two (or more) components with different molecular diffusivities which contribute in opposing senses to the vertical density gradient. A hallmark of double-diffusive convection is the existence of layers separated by relatively thin interfaces. Due to turbulent convection the components are fairly uniform throughout each layer. I n the interfaces there are strong property gradients and molecular diffusion is important. In order to investigate many of the fundamental aspects of the motion in the layers or the transfer of properties through the interfaces it is often convenient to pre-set the layer depths, and many theoretical and experimental investigations have done this. Alternatively, a few different situations have been investigated in which the layer depths result directly from the double-diffusive process and have to be calculated or measured. The first example in the literature of this alternative approach is the qualitative experiment of Turner & Stommel (1964), followed by the quantitative investigation of Turner (1968). The situation Turner & Stommel considered was the application of a heat flux to the bottom of a column of water stably stratified with salt. They observed that a turbulent mixed layer gradually built up from the bottom of the containing vessel. After some time a second layer was seen to form and grow above the first. At a later time a third layer appeared and so on. Turner argued that the first layer is the direct response to the applied heat flux and that ahead of its advancing front a thermal 0022-ll20/79/4328-7800 $02.00 0 1979 Cambridge University Press