597 



admitted right at the beginning that these experi- 

 ments are still largely qualitative, and that much 

 more remains to be done , but already they suggest 

 new explanations of some existing observations in 

 the ocean , and allow us to predict what might be 

 measurable in future work. 



2. ONE-DIMENSIONAL PROCESSES 



Formation of Layers from a Gradient 



For completeness, the fundamental physics of the 

 double-diffusive convection will be outlined briefly 

 by referring to the simpler early experiments. The 

 review of one-dimensional experiments will then be 

 brought up to date and specific oceanographic 

 examples of these processes will also be described. 



The necessary conditions for double-diffusive 

 convection to occur in a fluid are firstly that 

 there should be two or more components having 

 different molecular dif fusivities, and secondly 

 that these components should make compensating 

 contributions to the density. It is remarkable 

 that under these conditions strong convective 

 motions can arise even when the net density distri- 

 bution increases downwards. The overall density is 

 'statically stable' in this sense in all the cases 

 described here. Motions are nevertheless generated 

 since the action of molecular diffusion, at different 

 rates for the two components, makes it possible to 

 release the potential energy in the component which 

 is heavy at the top. This can drive convection in 

 relatively well-mixed layers, while the second 

 (stably distributed) component preserves the density 

 difference across the interfaces separating them. 



There are two cases to be considered, depending 

 on the relation between the dif fusivities and the 

 density gradients, i.e., on whether the driving 

 energy comes from the component having the higher 



or lower diffusivity. The simplest example of 

 the former is a linear stable salinity gradient, 

 heated from below. An unstratified tank would over- 

 turn from top to bottom, but because of the stabi- 

 lizing salinity gradient only a thin temperature 

 boundary layer is formed at first, which breaks 

 down through an overstable oscillation [Shirtcliffe 

 (1967)] to form a shallow convecting layer. This 

 layer grows by incorporating fluid from the gradient 

 above it, in such a way that the steps of S and T 

 are nearly compensating, and there is no disconti- 

 nuity of density, only of density gradient. 



When the thermal boundary layer ahead of the 

 convecting region reaches a critical Rayleigh number, 

 it too becomes unstable. A second layer then forms 

 above, and eventually many other layers form in 

 succession (See Figure 1) . The vertical scale of 

 these layers increases as the heating rate is 

 increased, and decreases with larger salinity gra- 

 dients. Turner (1968) has shown that the first 

 layer stops growing when 



d„ = D B 



3A 



(1) 



FIGURE 1. Layering produced from an initially 

 smooth salinity gradient by heating from below. 

 Three well-mixed layers are marked by fluorescein 

 dye, lit from the top. (Tank diameter, 300mm.) 



constant which depends on the critical Rayleigh 

 number and the molecular properties, B = -gaFrp/pC 

 is the imposed buoyancy flux corresponding to a 

 heat flux Fip (a being the coefficient of expansion 

 and C the specific heat), and Ng = [(g/p) (dp/dz]*! 

 is the initial buoyancy frequency of the stabilizing 

 salinity distribution. The criterion for the for- 

 mation of further layers is currently being studied 

 by Huppert and Linden (personal communication) . 



A device which has proved very helpful in elim- 

 inating uncontrolled sidewall heat losses (as well 

 as providing results directly relevant to the ocean) 

 is to carry out experiments with two solutes, say 

 sucrose and sodium chloride solutions, instead of 

 salt and heat. Essentially the same phenomena can 

 be observed, although the dif fusivities are much 

 more nearly equal (the ratio x = Kg/K-j, where <rp 

 denotes the larger and Kg the smaller diffusivity 

 in each case, is about 1/3 for sugar and salt, 

 compared with = 10~^ for salt and heat) . 



Linden (1976) has in this way extended the 

 "heated gradient" experiments to study the case 

 where there is a destabilizing salt (T) gradient 

 partially compensating the stabilizing sugar (S) 

 gradient in the interior. He has shown, both 

 theoretically and experimentally, that during the 

 formation of layers the relative contributions of 

 the energy provided by the boundary flux, and that 

 released in the interior, change systematically 

 with the ratio of the vertical T and S gradients. 

 In the limit where these gradients become equal, 

 all the energy comes from the destabilizing compo- 

 nent in the interior, and the ultimate layer depth 

 is finite and proportional to N^-h (where Ng is the 

 buoyancy frequency corresponding to the stabilizing 

 component) . 



Once layers and interfaces have formed, it is 

 important to understand what governs the fluxes of 

 S and T across them. For this purpose two or more 

 layers can be set up directly, and the interfaces 

 examined using a variety of optical techniques. 

 For example. Figure 2 is a shadowgraph picture of 

 a very sharp interface formed between a layer of 

 salt solution above a layer of sugar solution, which 

 is equivalent to colder fresh water above hot salty 

 water. Note that salt is here the analogue of heat. 



