(see Section II, 7) (e.g., Tung and Huang, 1974; Tayfun, Dalrymple, and 

 Yang, 1976; and Hedges, I98I). These spectra all show singularities at 

 the frequency of zero total group velocity (i.e., u + C = 0). Harper 

 (1980) deals with the mathematical problem that is implied by these 

 singularities. If the total group velocity is zero, then any property 

 related to wave energy remains at the wave sensor and accordingly gives 

 an anomalously high reading. Harper (1980) illustrates this by 

 considering measurements from a moving carriage. 



It is only for special circumstances, such as waves in a channel, 

 that simple general spectral calculations are possible. As is indicated 

 in the discussion of refraction (Section II, 4), it is the propagation 

 paths of the wave energy which are important, and these differ for 

 each frequency and direction. Forristall, et al. (1978) found that a 

 detailed hindcast of a directional spectrum, taking account of differing 

 propagation paths, gave good agreement with measurements. 



There are two major effects of a current on wave generation by wind. 

 First, the relative velocity between air and water is either increased 

 or decreased; thus a wind has a stronger effect when there is a current 

 opposing it. See, for instance, Kato and Tsuruya (1978a, b). This 

 particular phenomenon has been observed in satellite photographs of the 

 ocean surface by Strong and DeRycke (1973). These photographs show the 

 Gulf Stream quite clearly because of extra sun glitter due to the 

 greater surface roughness on the current. This surface roughness has 

 value in remote sensing, particularly when infrared observations can 

 show no temperature differences between water masses. The authors 

 illustrate this point with a photograph of the major current into the 

 Gulf of Mexico through the Yucatan Channel. 



The other major effect is a change in the effective fetch of the 

 wind since the wave energy travels at the vector sum of the current and 

 the group velocity relative to the current. For following currents, the 

 effective fetch is diminished; for opposing currents, it is increased. 

 For example, in a laboratory wind wave flume where wind and current are 

 in the same direction, wave energy reaches the end of the flume quicker 

 than in still water; hence with less duration for growth, the waves do 

 not grow as high as waves with the same relative wind over still water. 

 Waves on an opposing current spend more time under the wind and grow 

 correspondingly larger. Laboratory experiments of this type are 

 described by Kato and Tsuruya (1978a, b). 



On the open sea the same effects occur, but in most circumstances, 

 there is the added complication that much of the wave energy will have 

 propagated from other parts of the sea with different currents. In that 

 case, wave refraction, the topic of Sections II, 4 and 5, must be 

 considered. 



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