Streetj Chan and Fromm 



4.3. Prognosis 



The successful application of the SUMMAC technique to 

 several physical problems indicates its usefulness as an engineering 

 research tool for analyzing the dynamics of water waves in two space 

 dimensions. It is capable of providing accurate quantitative results 

 as well as qucilitative descriptions [see, e.g. , Chan and Street, 

 1970b] . In addition, rapid advance in the design of high-speed com- 

 puting systenas makes numerical modelling economically feasible. 



While it is possible to employ the SUMMAC technique to 

 attack a wide variety of water wave problems, some limitations 

 inherent in the method must be noted. First, as a result of achieving 

 a high degree of accuracy in applying the free surface pressure con- 

 dition by using irregular stars, waves after breaking cannot be simu- 

 lated. When breaking occurs, the computation must be terminated. 

 Second, only non- turbulent flows are considered in our model. 

 Although laminar viscous damping has little effect on large scale 

 wave motions, energy dissipation due to the turbulence can be sig- 

 nificant. However, a recent study by Pritchett [ 1970] shows that it 

 is feasible to imiplement a heuristic simulation of turbulence in the 

 MAC framework. 



ACKNOWLEDGMENT 



This research was supported in part by the Fluid Dynamics 

 Branch, Office of Naval Research, through Contract Nonr 225(71), 

 NR 062-320. 



REFERENCES 



Brennen, C. , "Somie Numerical Solutions of Unsteady Free Surface 

 Wave Problems Using Lagrangian Description of the Flow," 

 2nd International Conf. on Numer. Meth, in Fluid Dyn., 

 Berkeley, Calif, , Springer -Verlag, Pub., September, 1970. 



Camfield, F. E, , and Street, R. L. , "Shoaling of Solitary Waves 

 on Small Slopes," J. Waterways and Harbors Division, 

 ASCE, V. 95, No, WWi, Proc. Paper 6380, pp. i-22, 

 February, 1969. 



Carrier, G. F. , "Gravity Waves on Water of Variable Depth," J. 

 Fluid Mech. , Vol, 24, Pt. 4, pp. 641-660, April 1966, 



Chan, R. K. C. ,' and Street, R, L. , "A Computer Study of Finite- 

 Amplitude Water Waves," J. Compt, Physics, Vol. 6, 

 No. 1, August 1970 [1970a]. 



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