Piacsek 



recent colloquium at the National Center for Atmospheric Research in Boulder, 

 Colorado, several numerical experiments modeling some aspect of geophysical 

 fluid dynamics were presented [proceedings edited by G. M. Hidy (1966)]. In 

 addition, in the last few years many articles have been published on numerical 

 experiments concerned with specific model problems, or with specific numeri- 

 cal methods appropriate to such flow problems. 



The model experiments that numerical experiments have so far been 

 mostly concerned with may be divided into four groups: 



1. Convection between parallel vertical surfaces that are maintained at 

 different temperatures, in the absence or presence of rotation; 



2. Convection between parallel horizontal surfaces that are maintained at 

 different temperatures; 



3. Convection inside cumulus clouds; 



4. Wind-driven ocean circulations. 



The results of previous studies on these problems will be discussed in the 

 section below, where recent numerical results for a few specific problems are 

 also presented. A review of studies on numerical methods, mostly centered 

 on two-dimensional incompressible flows, will be given in the concluding 

 section. 



RESULTS FOR SPECIFIC MODEL EXPERIMENTS 



A. Thermal Convection in a Rotating Cylindrical Annulus 



This problem considers the convective flow of a liquid contained in a verti- 

 cal cylindrical annulus, and undergoing rotation about the cylinder's axis and 

 having differential heating in the horizontal. The temperature contrast is ap- 

 plied by maintaining the vertical cylindrical walls, assumed to be perfect con- 

 ductors, at different but uniform temperatures. The bottom surface of the 

 container and the free top surface of the liquid are considered to be thermal 

 insulators. 



The annulus experiments were introduced by Hide (1952, 1953) in the hope 

 of leading to a better understanding of convection in the earth's liquid core and 

 the related generation of the earth's magnetic field. The resultant flow phe- 

 nomena resembled those obtained in a rotating dishpan by Fultz (1953), whose 

 experiments were designed to simulate atmospheric motions. In both cases 

 the observed flow patterns appeared to have their counterparts in the general 

 atmospheric circulation, and to have similar physical processes among their 

 causes. Thus, the axisymmetric flow seemed to resemble a Hadley cell, pro- 

 posed by Hadley (1735) to explain the general trade winds, and to be due to 

 deflection by Coriolis forces of the north- south convection currents into zonal 

 (east-west) motion. The nonaxi symmetric flow regime seemed to resemble a 

 Rossby (1949) wave pattern in which finite amplitude waves propagated about 



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