III. THE ANNOTATED BIBLIOGRAPHY 



1. ARTHUR, R.S., "Refraction of Shallow Water Waves: The Combined 

 Effect of Currents and Underwater Topography," Transactions of the 

 American Geophysical Union, Vol. 31, No. 4, Aug. 1950, pp. 549-552. 



Keywords. Current Depth Refraction; Currents, Opposing; Currents, Rip; 

 Historical Interest; Theory; Theory, Ray; Waves, Long; Waves on a Jet. 



Discussion. This early paper on wave-current interaction describes a 

 ray solution for shallow-water waves meeting a rip current. The inter- 

 action is treated as a refraction problem and rays are drawn for one 

 example. 



A beach of uniform slope and an arbitrarily chosen current 

 satisfying mass conservation are specified. The result shows the rays 

 concentrating at the center of the jetlike current for waves directly 

 incident against it; wave crests are also drawn. 



The author comments that he discontinues the calculation and 

 diagram in the neighborhood of caustics and that they and wave 

 diffraction modify the solution. He also notes that interaction of 

 currents with a sand bed also modifies the resulting wave pattern 

 because of the greater depth of the current's channel. 



The author makes an inconsistent approximation to obtain his 

 equation (4). The correct equation is obtained by adding terms in C in 

 equation (4) to the right-hand side of equation (3). Even so, it is 

 likely that the error in the ray diagram (Fig. 3) is small. The general 

 picture of rays concentrating wave energy toward the center of the 

 current is certainly correct. 



Coastal Engineering Significance. Despite the minor error in mathema- 

 tics and the relatively early date of this work, it is still an 

 interesting paper. The author recognizes the importance of diffraction, 

 and it is likely that his analysis is of little value for rip currents 

 because of these diffraction effects. However, the analysis provides 

 good insight into the general nature of the wave field on larger scale, 

 jetlike currents, such as ebb currents at tidal inlets. There are still 

 no more recently published ray diagrams (at time of writing in 1982) for 

 such a basic pattern of flow. 



2. BARBER, N.F., "The Behaviour of Waves on Tidal Streams," 

 Proceedings of the Royal Society, London, England, Series A, Vol. 

 198, No. A 1052, July 1949, pp. 81-93. 



Keywords . Continental Shelf; Current Depth Refraction; Currents, Large- 

 Scale; Currents, Nearshore; Currents, Tidal; Currents, Unsteady; Wave 

 Observation; Wave Period. 



