Particular simple examples are briefly indicated, and it is noticed 

 that assumed properties of the current are also constrained by the 

 shallow-water approximation. 



Coastal Engineering Significance . This paper compares and shows the 

 relation between equations derived from an averaged Lagrangian and from 

 averaging equations of motion. The relations for wave properties are 

 for exact finite-amplitude periodic solutions. The equations presented 

 here form a good starting point for simplifying assumptions, or for 

 constructing numerical approximation schemes for current and depth 

 refract ion. 



55. TAYFUN, M.A., DALRYMPLE, R.A., and YANG, C.Y., "Random Wave-Current 

 Interactions in Water of Varying Depth," Ocean Engineering , 

 Pergamon Press, Oxford, England, Vol. 3, 1976, pp. 403-420. 



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

 Shearing; Currents, Unidirectional; Spectra; Spectra, Directional; 

 Theory; Theory, Ray; Wave Action. 



Discussion . The properties of wave rays in depth and current varying 

 conditions are reviewed and applied to a representation of wave direc- 

 tional spectrum. There is discussion of the transformation of direc- 

 tion, wave action, and wave energy as well as how rays may terminate due 

 to wave breaking or reflection. The analysis is restricted to linear 

 theory. 



Details of analytical solutions are given for cases with unidirec- 

 tional currents, including deepwater waves on a shearing current and a 

 combination of depth and current refraction in shallow water. The 

 details are plotted in a frequency-direction diagram. This procedure 

 has advantages since the absolute frequency of each wave component 

 remains constant on the steady currents considered. This is a straight 

 forward extension of well-established results obtained by adding the 

 results for each Fourier component. However, the discussion and presen- 

 tation place the theory in a slightly different context. 



Coastal Engineering Significance . The initial discussion makes this 

 paper a reasonable starting point for engineering applications. The 

 examples could be used for verifying computer programs. 



56. TUNG, C.C, "Peak Distribution of Random Wave-Current Force," 

 Journal of the Engineering Mechanics Division, Vol. 100, No. EM5, 

 1974, pp. 873-884. 



Keywords. Forces on Cylinders; Spectra; Statistics. 



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