599 



has shown theoretically that an intermediate layer, 

 or series of layers, is stable if the overall S 

 and T differences lie in the range where the flux 

 ratio is constant, and unstable if the flux ratio 

 varies with Rp . Observations of stable layers in 

 the ocean seem to be consistent with this criterion. 

 The merging of layers by this and other mechanisms 

 has been studied experimentally by Linden (1976) . 



Some measurements have also been made in the 

 case where several solutes with different diffusivi- 

 ties, Kjj' ^^s driven across an interface by heating 

 from below. Turner, Shirtcliffe, and Brewer (1970) 

 showed that the individual eddy-transport coeffi- 

 cients can be different, and suggested that they 

 are proportional to Kjj'S. More recent work by 

 Griffiths (personal communication) predicts theo- 

 retically that the ratios of transports of pairs 

 of solutes should be proportional to x^ at low 

 solute-heat density ratios, and to t at higher 

 ratios. His much more accurate and extensive 

 experiments show an even larger variation, for 

 reasons which are still unexplained. These results 

 are potentially of great importance for the inter- 

 pretation of geochemical data, as will be discussed 

 further below. 



Observations of Diffusive Interfaces 



There are now many observations of layering in the 

 ocean which can unambiguously be associated with 

 "diffusive" interfaces, and where a one-dimensional 

 interpretation seems appropriate. The regularity 

 of the steps and the systematic increase of both 

 S and T with depth serves to distinguish these from 

 layers produced in other ways (by internal wave 

 breaking, for example) . Neal et al. (1969) and 

 Neshyba et al. (1971) have observed layers about 

 5 m thick, underneath a drifting ice island in the 

 Arctic where cold fresh melt water overlies warm 

 salty water. A common observation in Norwegian 

 fjords is that cold fresh water, formed by melting 

 snow, can often form a thin layer on top of warmer 

 seawater, with an interface which remains extremely 

 sharp, and thickens much less rapidly than expected. 

 This is due to double-diffusive convection driven 

 by the heat flux from below, which will stir the 

 layers on each side of the interface (independently 

 of any wind stirring at the surface) and thus keep 

 the interface sharpened. 



There are also fresh-water lakes in various parts 

 of the world which have become stratified in the 

 past by the intrusion of sea water. Some of these 

 are heated at the bottom by solar radiation, and 

 convectively mixed layers separated by diffusive in- 

 terfaces are formed. A particularly well-documented 

 example is Lake Vanda in the Antarctic [Hoare (1968) , 

 Shirtcliffe and Calhaem (1968) ] . Since these lakes 

 are not complicated by horizontal advection pro- 

 cesses, Huppert and Turner (1972) were able to 

 use the Lake Vanda data to show that the one- 

 dimensional laboratory result (3) can be applied 

 quantitatively to comparable large-scale motions. 



Other striking examples are the multiple steps 

 observed in a lake in the East African Rift zone, 

 which is heated geothermally by the injection of 

 hot saline water at the bottom [Newman (1976)], 

 and the layers of hot salty water found at the 

 bottom of various Deeps in the Red Sea [Degens and 

 Ross (1969)]. These layers are nearly saturated 

 with salts of geothermal origin, including a high 



proportion of heavy metals, and are of special 

 interest because of the potential commerical value 

 of the associated thick sediments. [Another related 

 application, to the genesis of ore deposits on the 

 sea floor, has recently been proposed by Turner and 

 Gustafson (1978)]. 



The existence of many components in these layers 

 raises another question which should be explored 

 more systematically in the oceanic context. 

 Griffiths' laboratory measurements mentioned above 

 indicate that different solutes are transferred 

 across diffusive interfaces at different rates, 

 depending on their molecular dif fusivities. The 

 "mixing rate" for a tracer is thus not necessarily 

 a good indicator of the transport of a major com- 

 ponent if interfaces are important. In the absence 

 of definite knowledge of the mixing mechanisms 

 which have operated between the sources and the 

 sampling point, the assumption that all components 

 are mixed simultaneously (i.e., that a single "eddy 

 diffusivity" should be used) seems likely to lead 

 to large errors, and even to gross misinterpretations 

 of geochemical data. 



Double-diffusive processes can also be important 

 in other systems besides aqueous solutions. A 

 situation of oceanographic interest arises if liquid 

 natural gas (LNG) or some other liquid gas spills 

 (following a tanker accident for instance) onto 

 the sea surface [Fay and MacKenzie (1972)]. The 

 liquid quickly evaporates to form a layer of cold 

 gas, predominantly methane, which would be lighter 

 than the air above it except that it is much colder. 

 Since methane, and also water vapour picked up from 

 the sea surface, have larger dif fusivities than heat 

 in air, double-diffusive effects can again be 

 important in this gaseous system. The driving 

 energy comes from the distribution of methane and 

 water vapour, so the interface is "diffusive". 

 The limited observations available suggest that 

 the top of such a layer is very sharp, and its rate 

 of spread vertically small, which is consistent 

 with a self-stabilizing double-diffusive transport 

 across the interface. Another application, to 

 explain the phenomenon of "rollover" in LNG storage 

 tanks, will not be described in detail here, but it 

 too depends on double-diffusive effects, this time 

 in the liquified gas [see Sarsten (1972) ] . 



Salt Fingers and Related Phenomena 



We now turn to the second type of doioble-dif fusive 

 convection, that for which the driving energy is 

 derived from the component having the lower molecular 

 diffusivity. Though this is associated with the 

 very different phenomenon of "salt fingers", there 

 are many similarities between it and the "diffusive" 

 case already presented, and these will be emphasized 

 in the following discussion. 



When a small amount of hot salty water is poured 

 on top of cooler fresh water, long narrow convection 

 cells or "salt fingers" rapidly form. These motions 

 were first predicted by Stern (1960) [and see Stern 

 (1975) for a more up to date account of the theoret- 

 ical work] . They are sustained by the slower 

 horizontal diffusion of salt relative to heat, which 

 permits the release of the potential energy in the 

 salt field. Again, fingers may be produced using 

 two solutes with much closer dif fusivities, and 

 when there are strong contrasts of properties, the 

 fingers are confined to an interface. Figure 4 



