Experiments on Convective Flows in Geophysical Fluid Systems 



the axis, similar to the Rossby waves found superposed on the zonal atmos- 

 pheric circulation. The causes for both the laboratory and atmospheric waves 

 are the growing perturbations due to baroclinic instability, as discussed by 

 Lorenz (1955), Eady (1949), and Charney (1947). Recently, similar phenomena 

 have been observed in the circulation of the solar atmosphere by Ward (1965), 

 adding astrophysical significance to these modelling experiments. 



Hide (1958), Fultz (1959), and Fowlis and Hide (1965) have studied the transi- 

 tion between the symmetric and wave regimes, and found that below a certain ro- 

 tation rate no waves can occur. Above this critical rotation rate the flow is sym- 

 metric for very small or very high temperature contrasts, with waves forming 

 for intermediate values. The value of the critical rotation rate and the range of 

 temperature contrasts for which waves occur depends on the geometry of the 

 container and the properties of the fluid; the latter also depend on the actual ro- 

 tation rate. They also found that the number of lobes forming the wave increased 

 with increasing rotation, but decreased with increasing heat contrast. Theoreti- 

 cal studies to predict the stability curve in parameter space has been performed 

 by Brindley (1960), Lorenz (1962), Barcilon (1964), and Merilees (1967). Although 

 they obtained a general qualitative agreement with the experimental curve, a 

 quantitative agreement left much to be desired. , - 



A detailed laboratory study of the temperature field and heat transfer, along 

 with qualitative velocity measurements, has been performed by Smith (1958), 

 Bowden and Eden (1965), and Eden and Piacsek (1968), for the upper symmetric 

 regime of flow (large heat contrast). These studies showed that the flow set up 

 strong boundary layers and a strong, stabilizing, vertical temperature gradient. 

 The isotherms were found to be horizontal in the interior for the case of small 

 or vanishing rotation rate, and to slope upward to the cold wall for high rotation 

 rate. There was a noticeable transition from stratification-controlled flow to 

 rotation-controlled above a critical rotation rate. A reversal occurred in the 

 radial temperature gradient near the cylindrical walls, and this effect disap- 

 peared gradually for increasing rotation rates. At any given radial distance 

 from the walls, the temperature deviation from the respective wall temperature 

 was found to be an exponential function of height over a major portion of the 

 flow, including the boundary layers. This variation with depth was different for 

 the high and low rotation cases, indicating the transition between flow regimes, 

 and also in the upper and lower regions of the fluid, indicating the possible ex- 

 istence of two convective cells. The experiments also revealed the strong effect 

 that the cylindrical geometry has on the flow: the height at which the mean iso- 

 therm traversed the gap was found to occur close to the bottom, and the heat 

 transfer varied with rotation as log (1/n^''^). 



To obtain a quantitative picture of the velocity field and the extent to which 

 the different transport processes contribute in the various regions of the flow, 

 Piacsek (1966, 1968), Quon (1967), and Williams (1967) independently have car- 

 ried out a series of numerical experiments in the axisymmetric regime of flow. 

 All of Quon's results and all but two of Williams' applied to flows with a rigid 

 lid in contact with the top surface of the liquid. Since the above laboratory ex- 

 periments were performed with a free top surface, only the relevant cases of 

 Piacsek and Williams will be discussed. 



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