Amsterdam, The Netherlands, 1978(b), pp. 162-203. (See also Report 

 No. S15, Danish Center of Applied Mathematics and Mechanics 

 (DCAMM), May 1979.) 



Keywords. Conservation Equations; Current Depth Refraction; Currents, 

 Large-Scale; Mass Transport; Review; Theory; Theory, Ray; Wave Action; 

 Wavelength. 



Discussion. The scope of this survey is to provide the necessary engi- 

 neering background for calculating the lengths, directions and heights 

 of sea waves propagating over a water area with an arbitrary large-scale 

 current distribution and bottom topography. So the emphasis is on so- 

 called current depth refraction, and a general procedure for solving 

 this problem is outlined. The survey begins by presenting a number of 

 wave phenomena, where interaction with currents is important. Large- 

 scale currents are considered, i.e., currents which only vary signifi- 

 cantly over many wavelengths. The same is assumed for water depths. 

 Only regular and nonbreaking waves are studied. 



Wavelengths are determined by wave crest conservation, and direc- 

 tions of wave travel by the orthogonal equation, which is presented. 

 The flux of wave action between neighboring wave rays, properly reduced 

 because of dissipation, then determines the wave heights. It is 

 stressed throughout that there are three sets of characteristic curves 

 in the general case of current depth refraction: streamlines, wave 

 orthogonals, and wave rays. It should have been emphasized, however, 

 that the wave rays are the primary curves. They can be calculated one 

 at a time from initial conditions and will then determine the orthogonal 

 field. In general, the opposite cannot be done. 



The complete set of depth-averaged conservation equations for mass, 

 momentum, and energy are given in three dimensions, including bottom 

 friction and the corresponding energy dissipation. It is further shown 

 how wind stress and horizontal turbulent shear forces can be included in 

 vertical sections. 



The energy equation is given both in the traditional form with the 

 radiation stress appearing, and in wave action conservation form, thus 

 introducing the wave ray. In the latter case the dissipation term takes 

 a special simple form, similar to wave action. 



Three special cases are discussed in detail: pure current 

 refraction, straight coastline, and inflow from the sides. 



Normally, the wave transformation is calculated on a given current. 

 Here an attempt has been made to find criteria when the wave feedback on 

 the undisturbed current is important. The discussion is incomplete, 

 though, since the often significant increase in current bed shear, due 

 to the wave motion, is not mentioned explicitly. 



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