when measuring uniform profiles on infinite beaches, they provide the ideal 

 controlled environment for the much-needed data to check two-dimensional, 

 nearshore circulation models. This is true for both the models based upon 

 radiation stress theory discussed above and the newly emerging Boussinesq 

 theory numerical models. 



IV. BOUSSINESQ THEORY 



Limitations in the range of application of Boussinesq theory compared 

 with cnoidal and stream- function wave theories were shown in Figure 44. 

 Here, those few examples of numerical solutions of the Boussinesq equations 

 versus experimental results that have been published are presented. Also, 

 the fact that a numerical theory carries with it inherent accuracy limitations 

 based upon the numerical integration methods, grid sizes, and time steps 

 used in the calculation is emphasized. Differences between theory and 

 experiment may also be due to the poor choice of a numerical method with 

 large truncation errors. 



1. Wave Shoaling . 



One-dimensional wave shoaling studies (solitary and periodic) were 

 conducted first. Early pioneering efforts by Peregrine (1967)^"^, Camfield 

 and Street (1969)^^, Madsen and Mei (1969)'^^, Madsen, Mei, and Savage 

 (1970)72^ and Chan and Street (1970)"^ concentrated on the physics of soli- 

 tary and periodic wave propagation (nonpermanent form, soliton development) 

 rather than accuracy of numerical versus experimental data. For example. 

 Figure 83(a) shows the calculated shoaling curves for a solitary wave ,_ 

 (rio/d = 0.1) on three different beach slopes by Madsen and Mei (1969) 

 compared with some experiments by Camfield and Street (1969)^^ for 



52pEREGRINE, op. ait. 



^^CAMFIELD and STREET, op. ait. 



'^^MADSEN and I'lEI, op. ait. 



''^MADSEN, O.S., MEI, C.C., and SAVAGE, R.P., "The Evolution of Time-Periodic 

 Long Waves of Finite Amplitude," Journal of Fluid MeahaniaSj Vol. 44, Pt. 1, 

 1970, pp. 195-205. 



SOCHAN and STREET, op. ait. 



""^Ibid. 



^^Ibid. 



210 



