This nonlinear aspect implies that these computations are not exactly 

 reversible. Projecting a wave condition offshore without dissipation from a 

 measurement site to djjj can result in a markedly different computed dissipa- 

 tion rate there than if the nominally corresponding waves are projected 

 onshore to djj. However, the calculation procedure tends to cancel internally 

 this effect of nonlinear height dependence. 



Reversing Example Problem 2, using H^ = 1.69 meters at di = 9 meters as 

 the initial conditj^on, computed conditions at dm include Cm = 1.24 meters, 

 ^em ~ 0.0406 and Em = 7.52 kilograms per second cubed, but at dj = 5.2 meters 

 the calculated wave height is 1.67 meters, only 1.8 percent less than the near- 

 shore wave height of 1.7 meters originally specified. Using computed final 

 wave heights in Example Problem 1 as input conditions, the reverse calculation 

 procedure gives wave heights in each case only .2 percent less than the specified 

 height of 3.5 meters. 



Such slightly irreversible results do not seem too significant for potential 

 applications. However, the Appendix to this report provides a calculator 

 program quickly executing the present procedure, making it convenient to 

 examine results of reverse calculations and to determine a wave condition which 

 appears optimally consistent with that specified. 



IV. SUMMARY 



The equations and procedures presented here permit calculation of nearshore 

 wave height changes considering the energy dissipated by rough turbulent flow 

 over a strongly agitated bed of quartz sand. All elementary wave relationships 

 are from linear (small-amplitude) wave theory, but one effect of incorporating 

 dissipation is that calculated height changes depend on the actual wave height. 

 Example calculations demonstrate the conversion of a nearshore wave condition 

 into a corresponding wave height in shallower or deeper water; the present 

 procedures are suitable only for field waves of relatively large height and 

 period in fairly shallow water. The general effect of energy dissipation is 

 that nearshore wave height remains more nearly constant outside the breaker 

 zone than linear wave theory would predict. 



15 



