Experiments on Convective Flows in Geophysical Fluid Systems 



the latter have observed that when the surface was disturbed the radiation tem- 

 perature rose to that of the lowered thermistor, but it returned to its normal 

 value in about 5 seconds. From this cooling rate they estimated that the cold 

 layer must be --I mm thick. 



Since observations on such a small-scale phenomenon are difficult to carry 

 out at sea (because of waves, instrumentation, etc.), several workers have at- 

 tempted to isolate the phenomenon in the laboratory. Spangenberg and Rowland 

 (1961) studied evaporative cooling by taking schlieren photographs simultaneously 

 from the top and side of a tank of water. They found that the cooled surface 

 layer collects along lines, producing thickened regions which become unstable 

 and plunge in vertical sheets. These lines appeared to have no fixed dimensions 

 or geometric pattern, and their number per unit area appeared to depend on the 

 cooling rate rather than on the depth of the container. From the experimentally 

 observed nonlinear temperature profiles with depth, they have deduced a local 

 Rayleigh number of 1193 when convective circulation was started, and a Rayleigh 

 number (see the next subsection in this paper) of 102 for maintaining an estab- 

 lished circulation. The cells were always changing their shape and size, with 

 some drifting about, some fading away, and others replacing them, suggesting 

 some kind of turbulent behavior. The circulation in the cells was primarily 

 two-dimensional and appeared to be independent of the depth of the water layer 

 for depths greater than 1 cm. However, some temperature deviations were 

 measured as low as 4 cm below the surface. Foster (1965a) performed similar 

 experiments in which he measured the top surface temperature by an infrared 

 radiometer, and the onset of convective behavior by visual observations of a 

 thin layer of ink at the bottom of the water. He found that at large Rayleigh 

 numbers the time needed for the commencement of convection and the horizontal 

 wave number of the disturbances amplified most are independent of the depth of 

 the fluid layer. The convection cells appeared as roughly circular or polygonal 

 white spots in the ink layer, underneath descending columns of water. Berg, 

 Boudart, and Acrivos (1966) performed an elaborate study on natural convection 

 in pools of evaporating liquids. They found certain patterns to be due to surface- 

 tension-driven instability, and others due to buoyancy-driven motion. Water be- 

 haved differently from all the other fluids investigated; no convection at all was 

 observed until the depth of the layer reached 1 cm, and then it occurred in 

 sheets only. This anomalous behavior was attributed mostly to surface contami- 

 nation by surface- active agents which always seem to be present in water. Fos- 

 ter (1965b) has performed a theoretical analysis of the stability of an initially 

 homogeneous layer of fluid which is cooled uniformly from above, and found that 

 the onset time of the convection and the horizontal wave-number amplified most 

 are independent of the depth, but depend on the Prandtl number and the cooling 

 rate, thereby agreeing with the experimental results. 



Whitehead and Chen (1967) have studied the stability and finite amplitude 

 motion of a thin, thermally unstable fluid layer, bounded above by a rigid sur- 

 face and below by a stably stratified body of fluid. Observations made by top 

 and side shadowgraph views showed that the flow consists of intermittent jets 

 and sheets plunging downward. For stronger cooling rates, more sheets were 

 seen, similar to Spangenberg and Rowland's results. Gribov and Gurevich 

 (1957) have made a theoretical investigation of instabilities in a fluid layer that 

 is bounded above and below by stable fluid regions, but into which the 



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