Coastal Engineering Significance . This paper treats the question of 

 waves near caustics , a question that has often worried coastal 

 engineers. The results indicate two types of caustics, only one of 

 which leads to breaking. They also emphasize the wide range of 

 conditions in which caustics may be formed. 



45. PEREGRINE, D.H., and THOMAS, G.P., "Finite-Amplitude Deep-Water 

 Waves on Currents," Philosophical Transactions of the Royal 

 Society, London, England, Series A, Vol 292, No. 1392, Aug. 1979, 

 pp. 371-390. 



Keywords. Averaged Lagrangian; Caustics; Current Refraction; Currents, 

 Large-Scale; Currents, Opposing; Currents, Shearing; Group Velocity; 

 Wave Breaking; Wave Height; Waves, Finite-Amplitude. 



Discussion. Longuet-Higgins' (1975) accurate solution for periodic 

 deepwater waves of any steepness up to the highest is used with Whit- 

 ham's averaged Lagrangian method. Longuet-Higgins' numerical values are 

 fitted by simple rational functions, and solutions are found for two 

 current distributions. 



Waves on a current which has a shear in the horizontal direction 

 perpendicular to the current have a singularity in their solution for 

 small amplitudes, and no solution for stronger currents. There is also 

 a second, steeper solution for an appreciable range of currents before 

 this singularity is reached. This singularity corresponds to the neigh- 

 borhood of a caustic in the linear theory. The near-linear theory of 

 PEREGRINE and SMITH (1979) describes it as an R-type caustic at which it 

 is unlikely that waves will break. There is always a reflected 

 solution. 



For waves progressing directly against an adverse current, there 

 are solutions which progress smoothly up to the highest waves as the 

 magnitude of the current increases. More remarkably, the solution for 

 reflected waves ceases to exist for moderate initial waves. This is an 

 S-type caustic. It seems likely that water waves normally break in the 

 region of an S-type caustic. 



There is a section discussing how the concept of group velocity may 

 be extended to finite-amplitude waves. There are several different 

 possible definitions, and it is shown that most have different values 

 for a given train of water waves. No firm conclusions are drawn, though 

 some new stability results are presented. 



Coastal Engineering Significance . This paper shows how finite-amplitude 

 effects alter the amplitude of waves in the neighborhood of caustics. 

 In particular, it shows how the type of caustic that occurs on an 

 adverse current is more likely to lead to wave breaking. 



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