The existence of the so-called Stokes mass transport is discussed 

 in detail. 



A steady situation is considered throughout. It is explained, 

 though, how the energy equations transform if there is a time-varying 

 current . 



Shallow- and deep-water approximations are normally presented after 

 the general expressions. The effect of the current profile not being 

 vertically uniform is discussed in a special section, where linear 

 current profiles are considered. The tricky problem of allowable 

 boundary conditions is not treated. For irrotational flow this has been 

 discussed in Skovgaard and Jonsson (1976). 



Coastal Engineering Significance. This article is important because it 

 is published in an engineering text that will introduce the wave-current 

 interaction considerations to engineers not previously acquainted with 

 them. Tables and graphs are included to show wavelength changes due to 

 interaction with current. In particular, the "stretching" due to a 

 following current and the "compression" due to an opposing current are 

 demonstrated. 



26. JONSSON, I.G., and SKOVGAARD, 0., "Wave Refraction Across a 

 Shearing Current," Proceedings of the 16th Coastal Engineering 

 Conference, American Society of Civil Engineers, Vol. I, 1978, pp. 

 722-741 (see also Report No. 151, Danish Center of Applied 

 Mathematics and Mechanics (DCAMM) , Dec. 1978.) 



Keywords. Current Refraction; Currents, Large-Scale; Currents, Shearing; 

 Currents, Unidirectional; Setdown; Theory; Theory, Ray; Wave Filtering; 

 Wave Height, Wavelength. 



Discussion. The paper deals with the transformation of plane, monochro- 

 matic waves, as they cross a shearing current, where the current velo- 

 city changes from one value in region 1 to another in region 2. 



The object of the study is to determine the direction of 

 propagation, and the length and height of the wave motion in region 2. 

 This is done by applying Snell's law, and the conservation equations for 

 wave crests and wave action. Input parameters are water depth (assumed 

 constant), absolute wave period, angle of incidence, initial wave 

 height, and current velocities in the two regions. Amplitude effects 

 are disregarded, and the current gradient is assumed small. 



This is an extension of the work by LONGUET-HIGGINS and STEWART 

 (1961), who considered the special case of deepwater waves progressing 

 from still water into a region with a uniform current. Here the depth 

 is arbitrary, and also current velocities can be arbitrary on both sides 

 of the shear layer. 



33 



