Studies on the Motion of Viscous Flows— VI 



1\ 



/ 



( 1 : ■ 



Q*^ ^ STATE 2 



Fig. 1 - Schematic representation of 

 stabilization by the nnolecular diffu- < ■ ^' 



sion of salts »-'•' •, - 



vortex to rotate and transfer the heat and salts upward. After completing the 

 rotation to state 2, part of the heat and salts which diffused into point a in 

 state 1 are transmitted upward, while new quantities of heat and salts diffuse 

 into point b. However, because of the much smaller numerical value of the 

 coefficient of diffusion of salts as compared to that of diffusion of heat, an ex- 

 cess of the quantity of salts as compared with the quantity of heat will be 

 present at point a. For the same reason, the quantity of heat diffused in b will 

 exceed the quantity of salts at the same point. Consequently, because of the 

 buoyancy, a restoring momentum arises, turning the convective vortex in a di- 

 rection opposite to that of its original rotation. In this way, the delay of the 

 molecular diffusion of salts inhibits the rotation of the convective vortex and 

 causes an oscillating motion. Indeed, Mr. H.Weinberger (1962), has shown 

 analytically that in case (b) above, overstability can precede the convective 

 instability. 



As noted, case (c) has been considered in detail (Stern, 1960). It is inter- 

 esting to note the reversal of the phenomenon: as reported by Stern, in case 

 (c) internal gravity waves are inhibited in favor of convective instability, while 

 as shown here in case (b) convective instability is inhibited by means of over- 

 stable oscillations. The present theory may explain some interesting obser- 

 vations concerning the antarctic Lake Vanda. In the lower part of the lake 

 (Wilson and Wellman, 1962), from 170-ft depth down to the bottom of the lake, 

 a stable- stratified solution with gradients of salinity and temperature is ob- 

 served. Between 50 ft and 120 ft depth no gradients of temperature and sa- 

 linity are observed, and this part of the lake is most probably in a state of tur- 

 bulent convection. In the remaining two parts of the lake, from a depth of 

 about 125 ft down to 165 ft, and from 45-ft depth up to the ice level, starting 

 at about 10 ft, a small gradient of salinity seems to be stabilizing a larger 

 temperature gradient. Abnormally hot saline water has also been found in the 

 red sea (Swallow, 1965). However, from the limited data reported in this 

 case, it is not possible to distinguish regions of overstability. 



An attempt to investigate the results concerning case (c) in the laboratory 

 has not been successful (Turner and Stommell, 1964). This may be ascribed 

 to difficulties in simulating a virtually unbounded horizontal domain, with 



699 



