For discussions of some detailed aspects of the use of ray theory 

 for wave-current interaction, see Skovgaard and Jonsson (1976), Iwagaki, 

 et al. (1977), Christof fersen and Jonsson (1980), and Christof fersen (in 

 preparation, 1982). For a mathematical review of depth refraction see 

 Meyer (1979). Dingemans (1978, 1980) reviews both refraction and 

 diffraction. 



If a whole spectrum of waves is to be considered, then there is at 

 present no alternative to considering each frequency and direction band 

 separately, as is the case for depth refraction. Forristall, et al. 

 (1978) describe an example of current refraction where this has been 

 done with some success in an investigation of waves due to a tropical 

 storm. Tayfun, Dalrymple, and Yang (1976) consider the transformation 

 of a wave spectrum across a simple current shear combined with a depth 

 transition. Several authors have considered the effect of currents 

 parallel to the waves ( = O'v-tt) on spectra, e.g., Huang, et al. 

 (1972), Hedges (1979, 1981), and Burrows, Hedges, and Mason (1981). 



An alternative to matching local solutions to a ray solution at any 

 focus or caustic is to use a "parabolic" approximation. This 

 corresponds to a second approximation in the modulation rate of the 

 waves and usually implies a restriction to waves traveling within a 

 small angle of some given direction. The method is described well in 

 the context of ocean acoustics by Tappert (1977). It has advantages in 

 that it includes diffractive effects which is valuable if a ray solution 

 leaves an area too sparsely covered with rays. A parabolic equation for 

 water wave - depth refraction is derived and applied in Radder (1979). 

 Booij (1981) derives an equivalent of Berkhoff's (1972) linear wave 

 equation (see Meyer, equation 3.6, 1979) from which a parabolic equation 

 for wave-current interactions is found. 



It is possible to consider computation from the basic equations of 

 fluid motion. For short waves, this would be prohibitively expensive at 

 present, if possible at all. For long waves, with the usual long wave 

 approximations which effectively eliminate dependence on a vertical 

 coordinate, it is possible. As already mentioned, tide-surge 

 interactions can be modeled this way. The present state of this type of 

 calculation is discussed in Peregrine (1981b) which deals with 

 computational models of the North Sea and other seas around the British 

 Isles to the edge of the Continental Shelf. One such model is being 

 used on an operational basis with direct input from U.K. Meteorological 

 Office's computer forecasts to forecast storm surges on British coasts. 

 These computations include long wave-current interactions. The model 

 described by Davies (1981) goes further to include the variation of 

 velocity with depth. However, it too is a long wave model since 

 pressure is taken to be hydrostatic. 



A more versatile numerical model is that described by Abbott, 

 Petersen, and Skovgaard (1978) which uses Boussinesq's equations. 

 Although a long wave approximation is made in this model, some 

 dispersive effects are also included, and hence somewhat shorter waves 



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