ENERGY LOSSES OF WAVES IN SHALLOW WATER 



hy 

 William G. Grosskopf and C. Linwood Vincent 



I . INTRODUCTION 



The energy in ^n irregular wave train changes as the waves propagate from 

 deep water toward shore. Estimates of the total change in wave energy have 

 traditionally been made by multiplying a shoaling, refraction and friction 

 coefficient by an offshore significant wave height to yield the nearshore wave 

 height. Recent studies of wave spectra have provided a more detailed view of 

 the wave field and indicate that additional processes should be considered. 

 This report presents finite-depth wave height estimation curves, given an ini- 

 tial JONSWAP type of offshore spectral wave condition (Hasselmann, et al., 1973) 

 generated over a short fetch and incorporating finite-depth steepness effects 

 based on a study by Kitaigorodskii, Krasitskii, and Zaslavskii (1975). These 

 curves represent energy changes due to shoaling and an upper limit of energy 

 spectral density as a function of wave frequency and water depth. 



Research at the Coastal Engineering Research Center (CERC) and elsewhere 

 indicates steepness effects that lead to breaking in a shoaling wave field 

 lead to a major loss of energy in addition to that lost by bottom friction and 

 percolation. These effects can be incorporated into wave estimation curves in 

 a fashion similar to shoaling because the effects can be made a function of 

 depth. The effects of refraction, bottom friction, and percolation are not in- 

 cluded in these curves because they are site specific. The effects of bottom 

 friction and percolation will always be to reduce the estimated wave height. 

 These curves should be applied only in areas of nearly parallel bottom contours. 

 Consequently, refraction will also only reduce wave height. 



This report presents a method for estimating the significant wave height, 

 Hg, given the fetch length, F, the overwater windspeed, U^ (see U.S. Army, 

 Corps of Engineers, Coastal Engineering Research Center, 1981), and the water 

 depth, d, neglecting any additional wave growth in shallow water due to the 

 wind. The method differs from two recently reported methods — Seelig (1980), 

 who presents a method for predicting shallow-water wave height given deepwater 

 wave height, Hq, peak period, Tp, and bottom slope, m, and Vincent (1981), 

 who presents a method for calculating the depth-limited significant wave height 

 based on knowledge of the deepwater wave spectrum — but it does not supersede 

 the use of these other two methods. The report provides an alternate approach 

 to the problem of shallow-water wave estimation given the four quantities men- 

 tioned above. 



II. WAVE HEIGHT PREDICTION CURVES 



A series of JONSWAP spectra was generated numerically in deepwater condi- 

 tions for varying windspeeds and fetch length, and propagated into shallow 

 water over parallel bottom contours. A frequency-by-frequency calculation was 

 made at various depths shoreward applying independently the wave steepness 

 limitation criterion (Kitaigorodskii, Krasitskii, and Zaslavskii, 1975) and a 

 shoaling coefficient to each spectral component. If the shoaled wave energy 

 exceeded the limiting value, the limiting value was retained. A detailed ex- 

 planation of the methodology involved in this computation is presented in the 



