Keywords. Conservation Equations; Current Depth Refraction; Currents, 

 Large-scale; Currents, Nonuniform; Currents, Shearing; Flow, Irrota- 

 tional; Mass Transport; Mean Energy Level; Setdown; Theory; Theory, Ray; 

 Wave Height; Wavelength. 



Discussion. The refraction of small surface gravity waves on large- 

 scale currents over a gently sloping seabed are studied. Some results 

 are a generalization to three dimensions of those obtained in JONSSON, 

 SKOUGAARD, and WANG (1970). 



Assuming irrotational flow, the complete set of conservation 

 equations for combined current depth refraction is presented, correct to 

 second order in wave height, and solved in two special cases. 

 Dissipation is neglected. 



One case is two-dimensional flow, pure current depth shoaling, 

 studied previously in the above reference. Similar graphs for 

 variation in wavelength and height are given. 



The other is a straight coast with the current, irrotational or 

 rotational, running parallel with the straight and parallel depth 

 contours. In the former case it is shown that the current effects on 

 the orthogonals and rays are opposite: If one bends more, the other 

 bends less. 



As a start on wider classes of problems, a general solution 

 procedure for the refraction equations is sketched. Two equations for 

 the current wave setdown are derived. One which is general, and one 

 which only applies to progressive waves on a current. The velocity 

 potential for a three-dimensional current wave motion is given. 



Coastal Engineering Significance . The equations for current depth 

 refraction are solved in two situations, curent depth shoaling, and 

 refraction at a straight coast with the current parallel to the bottom 

 contours. The "bending" by the current of wave orthogonals and rays is 

 illustrated and discussed. New formulas for the current wave setdown 

 are derived. The neglect of dissipation means that wave height varia- 

 tions are only qualitatively correct and limit the applicability of the 

 setdown expressions. 



28. JONSSON, I.G., BRINK-KJAER, 0., and THOMAS, G.P., "Wave Action and 

 Setdown for Waves on a Shear Current," Journal of Fluid Mechanics, 

 Cambridge, England, Vol. 87, No. 3, Aug. 1978, pp. 401-416. 



Keywords. Averaged Lagrangian; Comparison of Theory and Measurement; 

 Conservation Equations; Current Wave Shoaling; Currents, Large-Scale; 

 Currents, Unidirectional; Currents, Vertical Shear; Dispersion Relation; 

 Mass Transport; Radiation Stress; Setdown; Theory; Wave Action; Wave 

 Energy. 



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