NUMERICAL EXPERIMENTS ON CONVECTIVE 

 FLOWS IN GEOPHYSICAL FLUID SYSTEMS 



Steve A. Piacsek 

 University of Notre Dame 

 Notre Dame, Indiana 



INTRODUCTION 



In the last two decades meteorologists, oceanographers, and astrophysicists 

 have been turning increasingly to the use of model experiments, both theoretical 

 and in the laboratory. In analogy with the wind tunnel modeling of aerodynamicists, 

 they hope to simulate the complicated motions exhibited by planetary and stellar 

 fluid systems by studying flows on a reduced scale, but being governed by the 

 same nondimensional parameters. These parameters depend on the properties 

 of the fluid, the imposed density contrasts, rotation of the container correspond- 

 ing to that of a planet or star, dimensions and shape of the container, and, in the 

 case of electrically conducting fluids, imposed magnetic fields corresponding to 

 planetary and stellar fields. 



The advantages of model experiments are the strict control that can be exer- 

 cised over the parameters determining the flow, and the possibility of isolating 

 the several concurring processes in order to study each separately. The disad- 

 vantages include working with fluids that do not approximate well some of the 

 natural systems, rigid boundaries that exert considerable control over the flow 

 but often have no counterpart in the geophysical processes, and the inability to 

 produce a spherical gravitational field in the laboratory. Furthermore, experi- 

 mental observations on flow details can be obtained only with difficulty, particu- 

 larly in the boundary layers. Visual studies using injected dyes and dye crystals, 

 and the use of interferometers and hot-wire probes give in many instances only 

 a qualitative or semiquantitative information on the velocity fields, particularly 

 in the case of liquids. Though reasonably accurate temperature measurements 

 have been obtained using thin thermocouples, even in the boundary layers, the 

 flow is known to be disturbed to various degrees by such probes or array of 

 probes. And because of the highly nonlinear nature of the governing equations, 

 purely analytical approaches have been made only with great difficulty, and only 

 for a limited range of the relevant nondimensional parameters. To overcome 

 these disadvantages, geophysicists have begun to rely more and more on numeri- 

 cal experiments, made possible by the advent of large and extremely fast digital 

 computers. 



Initial efforts in modeling fluid motions in geophysics were discussed at a 

 symposium at the Johns Hopkins University in 1953 (proceedings edited by R. 

 Long); at this meeting, no numerical experiments were discussed as yet. At a 



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