frequency than for still water. The discussion of slowly varying 

 currents is based on the conservation of wave-action equation, and three 

 different examples are discussed in detail. 



The first such example is for waves on a current which is unidirec- 

 tional and only varies in that direction. This is treated more 

 thoroughly than earlier work, including a discussion of possible caus- 

 tics at a "stopping point," nonlinear effects, and the behavior of waves 

 propagating at an angle to the current. Waves on a shearing, unidirec- 

 tional current are also given a similar thorough treatment. The non- 

 linear theory for both cases is carried further in PEREGRINE and THOMAS 

 (1979) and PEREGRINE and SMITH (1979). 



Another substantial section deals with waves on currents which vary 

 with depth. A number of results are drawn together, and present 

 deficiencies in the theory are noted. Unlike most of the other topics 

 in the paper, there are some experimental results available, but these 

 raise further questions. 



Shorter sections deal with currents that are smaller in scale than 

 the waves, with turbulence, and with the influence of the boundary layer 

 and the wake of a ship on ship-generated waves. 



Coastal Engineering Significance . This book-length review provides an 

 integrated overview of wave-current interactions. It gathers together 

 almost all the work in the field and discusses many topics in such a way 

 that both the results and limitations of present knowledge are exposed. 



43. PEREGRINE, D.H., and SMITH, R., "Stationary Gravity Waves on Non- 

 Uniform Free Streams: Jet-Like Streams," Proceedings of the Mathe- 

 matical Cambridge Philosophical Society, Cambridge, England, Vol. 

 77, No. 2, Mar. 1975, pp. 415-438. 



KeyT^ords. Caustics; Jetlike Streams; Waves, Stationary. 



Discussion. A variety of mathematical methods are employed in order to 

 describe stationary waves on currents. The currents are taken to be 

 "jetlike," i.e., uniform in direction but decaying in magnitude away 

 from some central line. They may or may not decay with depth or may be 

 symmetrical in the transverse horizontal direction. A feature of 

 stationary waves in these circumstances is that they are "trapped." 

 They cannot propagate off the current. In the case of waves considered 

 short when compared with the current scale, this means that they are 

 trapped between caustics. 



The problem is first considered generally for linearized waves and 

 shown to be an eigenvalue solution. An exact solution is given for a 

 uniform jet bounded by vortex sheets at the sides and below (a "top hat" 

 velocity profile). It simply illustrates the type of results to be 

 obtained. 



48 



