130 Shallow Water Wave Transformation through External Factors 



of wave motion, the total flow of energy between two orthogonais must 

 remain constant. Thus, if orthogonais converge, the crests are compressed, 

 and the energy per unit crest length is relatively large; if orthogonais diverge, 

 the crests are stretched, and the energy per unit crest length is relatively small. 

 It has been derived previously that the change in wave height, when the 

 waves enter into shallow water follows the relation 



I-VU?)- (v - 24) 



The breaking waves, with their sharp crests isolated by long flat troughs, 

 have the appearance of "solitary" waves (see pp. 116 and 121), for which the 

 height is proportional to the cube root of the energy. We then have, instead 

 of the relation (V.24), the relation 



— =—^ , (V.25) 



H 3-3 ViHM 



in which H /A is the slope of the wave or wave steepness in deep water. 

 These relations are only valid when the orthogonais are parallel, which is 

 to say with rectilinear propagation of waves. Munk and Traylor show that, 

 when the orthogonais are convergent or divergent, equation (V.25) must be 

 corrected with a factor which takes into account the variation in distance s 

 between two adjacent orthogonais. Let H designate the wave height and s 

 the distance between adjacent orthogonais on the refraction diagram. Para- 

 meters with subscript again apply in deep water, those with subscripts b 

 at the breaker point, and parameters without subscript at any depth inter- 

 mediary between deep water and the breaking point. 



jf = yK, ^ = y b K b , (V.26) 



where y and y b are the right-hand terms of equations (V. 24) and (V. 25) and 

 have constant values along a fixed depth contour 



K 



-j/^ and K b =j/ S j (V.27) 



vary along a depth contour and will be referred to as the "refraction factors". 

 Equations (V.26) are derived from the postulates that the energy flows 

 along orthogonais and that energy is conserved. This, in turn, implies two 

 assumptions : 



(1) The effect of diffraction (which would bring about the flow of energy 

 across orthogonais from regions of high waves to regions of low waves) 

 can be neglected. 



(2) The effect of bottom friction is negligible. The validity of these assump- 

 tions is borne out by the good agreement between computed changes in 



