Hirt 



Figure 6 shows a hydraulic jump at Reynolds number 79.25, The flow in 

 this case is no longer laminar. Large eddies have developed in the transition 

 region in an attempt to simulate turbulence. The calculations do not represent 

 true turbulence, because of the course resolution and the restriction to two- 

 dimensional flow. 



TURBULENCE 



It is interesting to speculate on the contributions that high-speed computing 

 can make to the understanding of turbulence. Three directions appear open to 

 numerical studies. The first is to use existing computing techniques to make 

 detailed studies of the breakdown and growth of laminar instabilities. Some 

 work on the stability of Poiseville flow has already been undertaken (8), Suc- 

 cess in these investigations will continue as the ability to calculate high Reyn- 

 olds number flows increases. 



The second approach is to calculate the detailed structure of a turbulence 

 flow. Such calculations will be extremely difficult, however, because they must 

 be done in three dimensions and require high resolution. Computers are too 

 slow and memory is too limited to permit much progress in this direction. 



The third possibility is to develop a capability to calculate the mean motion 

 of turbulent fluid, without regard to its detailed structure. In this approach the 

 turbulence is characterized by a small number of field variables. The variables 

 are postulated to satisfy transport equations that account for the processes of 

 production, decay, convection, and diffusion. A mean flow is influenced by an 

 exchange of energy with the turbulence and by turbulent diffusion of mean mo- 

 mentum. 



Although it is too soon to assess the full potential of this last approach, it 

 does appear highly promising. For further details, reference may be made to 

 the work of Harlow and Nakayama (9), 



ACKNOWLEDGMENT ' 



This work was performed under the auspices of the United States Atomic 

 Energy Commission. 



REFERENCES 



1. Harlow, F.H., Welch, J.E., Shannon, J. P., and Daly, B.J,, Los Alamos Sci- 

 entific Laboratory Report LA-3425 (1965); Harlow, F.H,, and Welch, J.E., 

 Phys, Fluids _8, 2182 (1965), and 9, 842 (1966) 



2. O'Brien, G.G., Hyman, M.A., and Kaplan, S., J. Math, Phys. 29, 223 (1950) 



3. Hirt, C,W,, J, Computational Phys, 2 (No, 4), 1968 



430 



