The results of the study are given in a number of dimensionless 

 graphs, between which interpolation can be made. Since the quantities 

 in the graphs may be difficult to read, and also because interpolation 

 is necessary, the calculation procedure is illustrated in an example. 

 It is shown to be quite simple. 



A physical discussion of the transforming effect of the shear layer 

 is given on the basis of a sequence of dimensional graphs. It is shown 

 that everything else being equal, wave height (and steepness) in region 

 2 has a minimum for a certain value of the current velocity in that 

 region. This is because a large positive current results in a refrac- 

 tion angle equal to 90 degrees, and so the wave rays tend to lie 

 infinitely close, resulting in (theoretically) infinite wave heights. 

 The waves are swept along the streamlines here. 



For a large negative current, the absolute group speed becomes 

 small, and since wave action flux (wave action times absolute group 

 speed) is constant, the result is high waves here also. This is the 

 first "filtering effect" shown: Both a large positive current and a 

 large negative current in region 2 can cause wave breaking. 



Another filtering effect is due to the fact that wave steepening 

 across the shear current is most pronounced for the short waves, and 

 therefore, the long waves pass through more easily. Isaacs (1948) 

 demonstrated this effect with a photo in which the breaking short waves 

 show up as a foam line. 



Physically possible solution domains are also given, as well as an 

 analytical expression for the (small) change in mean water level across 

 the shear layer. A horizontal bottom is assumed throughout. The calcu- 

 lations are easily extended, however, to the case of depth contours 

 running parallel to the streamlines. 



Dissipation due to the bottom friction and vortex formation in the 

 shear layer is neglected; however, the wave action conservation 

 principle for this situation is presented. 



An appendix provides general expressions for the determination of 

 wave orthogonals and rays, emphasizing the important difference between 

 these quantities. 



Coastal Engineering Significance . This paper is probably the first to 

 give an engineering formula for wave transformation across a shearing 

 current . 



27. JONSSON, I.G., and WANG, J.D., "Current-Depth Refraction of Water 

 Waves," Ocean Engineering^ Oxford, England, Vol. 7, No. 1, 1980, 

 pp. 153-171. (See also Series Paper No. 18, Institute of Hydrody- 

 namics and Hydraulic Engineering (ISVA), Technical University of 

 Denmark, Jan. 1978.) 



34 



