CALCULATION OF WAVE ATTENUATION DUE TO 

 FRICTION AND SHOALING: AN EVALUATION 



by 



Witlicm G. Gvosskopf 



I. INTRODUCTION 



Many processes are responsible for variations in the energy of nearshore 

 waves including breaking, friction, shoaling, refraction, percolation, and 

 nonrigid bottom effects. However, in an area where nearshore bottom contours 

 are straight and parallel, and bottom conditions indicate a nonpermeable and 

 nonelastic sea floor, wave breaking, shoaling, refraction, and friction remain 

 dominant. The area seaward of the pier end at U.S. Army Coastal Engineering 

 Research Centers 's (CERC) Field Research Facility (FRF), Duck, North Carolina, 

 meets these conditions. Data from FRF can be used to evaluate different for- 

 mulations of these processes. 



This report evaluates the Bretschneider and Reid (1954) theory recommended 

 in the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal 

 Engineering Research Center, 1977) for calculating the effect of bottom fric- 

 tion and shoaling on incoming waves, using data gathered from two offshore 

 Waverider buoy gages (manufactured by Datawell, Haarlem, The Netherlands) 

 located off the pier end at FRF. The two Waveriders operate in depths of 

 approximately 18 and 10 meters, at 2,880 and 680 meters from shore, respec- 

 tively. These instruments are located far enough offshore to avoid the 

 possibility of wave breaking, other than whitecapping, as a dissipative 

 mechanism between Waveriders for the data set used. Simultaneously observed 

 wave spectra from these two gages during 1978 and 1979 were compared to cal- 

 culated wave characteristics, using Bretschneider and Reid's (1954) prediction 

 for waves traveling over an impermeable bottom of constant slope. It is 

 found that Bretschneider and Reid's method provides a close correlation with 

 observed data, especially in cases where the wave spectrum is narrow and 

 single-peaked. 



II. CALCULATING CHANGES IN WAVE HEIGHT DUE TO BOTTOM FRICTION AND SHOALING 



Attenuation of wave height due to bottom friction- and shoaling can be 

 calculated using equation (1), for waves with significant wave height, H^, 

 wave period, T, traveling over a bottom of slope, m, and depth, d, at 

 the outer gage 1. Shoaling effects are calculated using linear theory. The 

 relation is 



-31 V' 



= K, K^ I — * + 1 (1) 



C^ H^ 

 mT^ 



s2 s si 



where 



C^ = friction coefficient 



K = shoaling coefficient 



m = bottom slope 



H 2 = significant wave height at nearshore gage 2 (Waverider gage 610) 



Yi , = significant wave height at outer gage 1 (Waverider gage 620) 



