602 



be mentioned here. In a two-layer system, in which 

 the layer depths vary because one wall of the 

 containing vessel is inclined, large-scale quasi- 

 horizontal motions can be set up even when the 

 buoyancy flux across the horizontal interface is 

 uniform. This effect is a purely geometrical 

 consequence of the sloping boundary. The net result 

 of the double-diffusive transports across the 

 interface is to provide an unstable buoyancy flux 

 which makes the bottom layer heavier. A given flux 

 produces more rapid density changes in shallower 

 regions where there is less dilution, and this sets 

 up a circulation in the sense which includes a flow 

 down the slope. Gill and Turner (1969) have shown 

 that this flow can reverse the relative gradients 

 of the two components, for example, giving rise to 

 salt fingers at the bottom of a tank originally 

 stratified in the diffusive sense. They have also 

 suggested an application to the formation of bottom 

 water near the Antarctic continent. Similar effects 

 have been observed by Turner and Chen (1974) when 

 a sloping interface, rather than a solid sloping 

 boundary, produces the non-uniformity of depth, 

 and this too can have implications for the formation 

 of bottom water in deeper water. 



FIGURE 6. Shadowgraph photograph of a melting ice- 

 block in a salinity gradient. Note the regularly spaced 

 scallops and ridges, caused by uneven melting asso- 

 ciated with the convection in layers. 



that the boundary conditions (on temperature or 

 salinity or both) do not match the conditions in 

 the interior. In tanks containing opposing gradients 

 of two components , with say a maximum salt concen- 

 tration at the top falling linearly to zero at the 

 bottom, and a maximum (slightly larger) sugar 

 concentration at the bottom falling to zero at the 

 top, the same kind of instability can be produced 

 in another way. With vertical side walls, the 

 surfaces of constant concentration are normal to 

 the boundaries, and the no-flux boundary condition 

 is automatically satisfied. But when an inclined 

 boundary is inserted, diffusion will distort the 

 surfaces of constant concentration away from the 

 horizontal, so that they become norm.al to the 

 boundary. Density anomalies are produced which 

 tend to drive flows along the wall; these cannot 

 remain steady, but instead turn out into the interior 

 and produce a series of layers. 



This process was first investigated experimentally 

 by Turner and Chen (1974) , with the initial strati- 

 fication in the "diffusive" sense. A prominent 

 feature of the intruding layers is the local reversal 

 of gradients in the extending "noses", where fingers 

 are prominent. In the later stages of that experiment, 

 the advancing noses have become independent of the 

 mechanism which produced them, and this suggested 

 the systematic study of double-diffusive sources 

 in various environments which is pursued below. 

 Linden and Weber (1977) have investigated layer 

 formation in the "finger" case; they have also 

 discussed the instability of the boundary layer 

 at the sloping wall, and the criteria determining 

 the layer depths. In the limit where the opposing 

 gradients are nearly equal, the characteristic 

 vertical lengthscale depends mostly on the initial 

 vertical distributions of S and T, and little on 

 the mechanism triggering the instability. 



A different effect of sloping boundaries should 



Double-diffusive Intrusions 



The experiments described in the two preceding 

 sections have recognized the importance of horizontal 

 gradients , but they still have not dealt with the 

 common situation where fluid with one set of T-S 

 properties intrudes into another having different 

 properties. This question has recently been 

 addressed by Turner (1978) , using sources of sugar 

 and salt solutions released into gradients of 

 various kinds. 



The basic intrusion process with which other 

 phenomena can be compared is the two-dimensional 

 flow of a uniform fluid at its own density level 

 into a linear gradient set up using the same property. 

 Figure 7 shows the behaviour of a (dyed) source of 

 salt solution released into a salinity gradient. 

 This is what we might intuitively expect: the 

 intruding fluid just displaces its surroundings 

 upwards and downwards, and is kept confined to a 

 horizontal layer by the denisty gradient. Detailed 

 studies of this process have been reported by 

 Maxworthy (1972), Manins (1976), and Imberger, 

 Thompson, and Fandry (1976) . Note praticularly the 

 "upstream wake" effect, leading to a considerable 

 disturbance of the environment ahead of the advancing 

 nose. 



When the source of salt is replaced by sugar 

 solution (S) , while the same salinity gradient (T) 

 is retained in the environment, the behaviour is 

 very different. (It is worth keeping in mind 

 throughout the following, the analogous situation 

 with temperature and salinity: this corresponds 

 to the intrusions of a layer of warmer, saltier 

 water into a stable temperature gradient) . As 

 shown in Figure 8, there is strong vertical convec- 

 tion near the source : this is produced by a 

 mechanism which also occurs with a uniform ambient 

 fluid close to the same density as that injected. 

 The more rapid diffusion of T relative to S across 

 the plume boundary causes it to become heavier, 

 and its immediate surroundings lighter, than the 

 fluid at the level of the source. The vertical 

 spread is limited by the stratification, and "noses" 

 begin to spread out at levels above and below the 



