and compares calculated and measured results. An example is given in Section 

 VI that applies the prediction methods to estimate nearshore significant wave 

 height. 



II. WAVE REFRACTION - DIRECTIONAL SPREADING OF WAVE ENERGY 



The confused sea state in deep water may be described as the sum of wave 

 trains simultaneously moving in various directions. As these wave trains move 

 toward the coast, the waves with the largest angles between their crest and the 

 bottom contours refract the most, so that nearshore waves appear to be less con- 

 fused. The reason for the directional spreading of wave energy in refraction 

 calculations for the case of straight parallel bottom contours is discussed in 

 this section. 



1. Directional Spreading of Wave Energy . 



Wave direction in deep water is difficult to measure, especially when many 

 wave trains of various energy levels are simultaneously moving in different 

 directions. However, a few basic measurements will help to quantify this di- 

 rectional spreading. Longuet-Higgins, Cartwright, and Smith (1963) suggest the 

 following density function for wave energy: 



Ycos(y)) 



E fl = K(cosra) S* (1) 



where 



6 = wave direction angle with respect to the dominant deepwater direction, 

 a (Fig. 1; note that a is measured from a line perpendicular to 

 the shoreline) 



K = a constant used to define the total wave energy 



Eg = the density of wave energy in a given direction, 



S* = a parameter that defines the variation of energy level with wave 

 direction. 



(Since the frequency dependance of directional spreading of wave energy is, of 

 secondary importance for diffraction (Goda, Takayama, and Suzuki. 1978) and re- 

 fraction calculations (Y. Goda, Director, Marine Hydrodynamics Division, Port 

 and Harbor Research Institute, Japan, personal communication, 1979) it is neg- 

 lected in this report.) Smaller values of S* yield higher amounts of direc- 

 tional spreading of wave energy. Goda, Takayama, and Suzuki recommend the values 

 of S* in Table 1 for design purposes. 



2. Refraction Calculations . 



Refraction calculations are based on the energy-weighted superposition 

 of refraction coefficients obtained from linear theory. If E£ and K#£ are 



10 



