601 



ensures that the effluent, diluted with many times 

 its volume of cold sea water, will spread out in a 

 layer below the thermocline. But this layer will 

 remain colder and fresher than the water above it, 

 so the salt finger mechanism can cause it to thicken 

 vertically, and even extend to the surface. A 

 related case, in which the environmental effects 

 could be even more serious, arises in the disposal 

 of effluent from a desalination plant. Suppose 

 that the brine from which water has been evaporated, 

 and the heated water from the cooling plant, are 

 mixed together to be disposed of as a single effluent. 

 This hot, salty water will have about the same 

 density as the original sea water - according to 

 the precise design conditions, it can be slightly 

 heavier or slightly lighter. If it is made heavier, 

 and forms a layer along the bottom, a diffusive 

 interface will be formed, and the coupled transports 

 will tend to increase the density difference and 

 thus keep the layer distinct. If it is put in at 

 the surface, or at an intermediate level in a 

 gradient, fingers will form, and there will be more 

 rapid vertical mixing. One thing is certain: the 

 rate of mixing cannot be determined using only the 

 net density distribution and leaving out of account 

 the double-diffusive effects. 



3. TWO-DIMENSIONAL EFFECTS 



Side-wall Heating and Related Processes 



It became clear in early laboratory experiments on 

 double-diffusive convection that layers will readily 

 form from a salt gradient in another way, if it is 

 heated from the side. This effect was studied 

 systematically by Thorpe, Hutt, and Soulsby (1969) 

 and by Chen, Briggs, and Wirtz (1971), and their 

 results can be summarized as follows. The thermal 

 boundary layer at a heated vertical wall grows by 

 conduction and begins to rise. Salt is lifted to 

 a level where the net density is close to that in 

 the interior; then fluid flows out away from the 

 wall, producing a series of layers that form 

 simultaneously at all levels and grow inwards from 

 the boundary. The layer thickness is close to the 

 length-scale 



aAT 



BdS/dz 



(6) 



which is the height to which a fluid element with 

 temperature difference AT would rise in the initial 

 salinity gradient. 



The stability problem corresponding to sidewall 

 heating of a wide container has not been solved, 

 though Stern (1967) has shown theoretically how 

 lateral gradients could lead to the generation of 

 layers. Thorpe, Hutt, and Soulsby (1969) have 

 analyzed the simpler case of a fluid containing 

 compensating linear horizontal gradients of S and 

 T, contained in a narrow vertical slot and Hart 

 (1971) improved their analysis; both theories 

 predict slightly inclined cells extending right 

 across the gap, with a spacing in fair agreement 

 with the measurements. 



Similar layers are formed when the salinity as 

 well as the temperature of the vertical boundary 

 does not match that in the interior, for example 

 when a block of ice is inserted into a salinity 

 gradient and allowed to melt. A qualitative experi- 

 ment of this kind was reported by Turner (1975) , 



FIGURE 5. Showing the tilted layers formed by insert- 

 ing a block of ice into salt-stratified water at room 

 temperature. Fluorescein was frozen into the ice, and 

 was illuminated from the side, so that the spread of 

 the dye indicates the distribution of the melt water. 

 (Negative print.) 



but interest in the process has increased recently, 

 because of the application to melting icebergs. 

 Huppert and Turner (1978) have carried out a more 

 extensive set of experiments with this problem in 

 mind. 



An understanding of the melting of icebergs 

 could be important in various contexts. Several 

 groups are currently examining the feasibility of 

 towing icebergs to their coasts and melting them 

 to provide fresh water, but there are many unsolved 

 scientific and engineering problems [see, for 

 example, Bader (1977)]. It has been proposed that 

 fresh water could be obtained by building a shallow 

 pen round a grounded iceberg, allowing the melt 

 water to collect in this, and siphoning it off the 

 surface. On the other hand Neshyba (1977) has 

 suggested that the melt water produced by icebergs 

 would mix with the surrounding sea water, and could 

 thus be effective in lifting water and nutrients 

 from deeper layers to the surface, where it would 

 increase biological production. 



Huppert and Turner's (1978) experiments have 

 shown, however, that neither idea is likely to be 

 valid, because of the neglect of the stable salinity 

 gradient which exists in the upper layers of the 

 oceans where icebergs are found. As demonstrated 

 in Figure 5, the presence of horizontal S and T 

 differences then produces a regular series of tilted 

 convecting layers, which feed most of the meltwater 

 into the interior; very little rises to the surface. 

 A more detailed analysis of the experiments is 

 continuing. At present it appears that for a 

 cooled sidewall the layer depths are similar whether 

 melting is occurring or not, and that they are not 

 described simply by (6) but depend more weakly on 

 the initial salinity gradient. Another phenomenon 

 which deserves more careful study is the series of 

 grooves and ridges produced by non-uniform melting 

 associated with the circulation in the layers (see 

 Figure 6) . 



Sloping Boundaries 



Phenomena analogous to those described above can 

 be observed in systems containing smooth gradients 

 of more slowly diffusing solutes. The essential 

 physical feature of the heated sidewall process is 



