PREDICTION OF WAVE REFRACTION AND SHOALING 

 USING TWO NUMERICAL MODELS 



by 

 Jon M. Huhertz 



I. INTRODUCTION 



This report discusses two numerical computer models which can be used to 

 estimate the refraction and shoaling of waves from deep to shallow water. The 

 models are based on the methods for estimating refraction due to bathymetry in 

 Section 2.3 of the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, 

 Coastal Engineering Research Center, 1977) but have features which make it 

 easier to obtain and interpret the results. Both models estimate wave height 

 and direction in a specified area when provided with an initial wave height 

 and direction on the boundary of the region. One model considers propagation 

 of a monochromatic wave along a ray; the other model propagates frequency com- 

 ponents of a wave spectrum. 



In the wave ray approach, the movement of a wave front is defined in terms 

 of rays perpendicular to the wave front. Wave heights are calculated along the 

 rays. The model which uses this method is documented by Poole, et al. (1977). 

 In the wave spectra approach, wave height and direction are available at grid 

 points over a specified area as a function of wave frequency. This model is 

 based on the work of Noda, et al. (1974) and described in detail by Wang and 

 Yang (1977). A modification of this program at CERC uses monochromatic wave 

 trains. The monochromatic version is used in this report; however, the spec- 

 tral version is available. 



A major difference between the two models is that in the wave ray approach, 

 values are available only along the rays. In the spectral model (used either 

 spectrally or monochromatically) , the wave values are available only at evenly 

 spaced grid points. 



II. APPLICATION OF MODELS 



Both models are based on linear wave theory and are limited by assumptions 

 which make that theory valid (see SPM, p. 2-6), Both models assume the con- 

 servation of wave energy. In the wave ray model, energy is conserved between 

 two adjacent rays; in the spectral model, energy is conserved within frequency 

 bands. This implies there is no flow of energy between waves of different fre- 

 quencies. The results of both models are valid only for monochromatic wave 

 trains. The effects of refraction and shoaling on waves of different fre- 

 quencies can be examined by making multiple runs. 



The most important input to either model is the bathymetry specified at 

 grid points over the region of interest. For best results, large variations 

 in depth should not occur over horizontal distances of about one wavelength. 

 It is easier to obtain bathymetry with these characteristics by using the 

 methods presented in Herchenroder (in preparation, 1981). The remaining input 

 to the models is a specification of wave height, period, and direction along 

 the models' seaward boundary. Lacking any measurements or first-hand knowledge 

 of deepwater wave conditions at a site, probable values for wave height and 

 period can be estimated from Thompson (1977) • Probable wave direction would 

 have to be estimated from other available sources of information; e.g.. 



