In still water, the measured wavelength agreed with theory, and the 



wave attenuation was somewhat greater than that predicted by Jonsson 



(1980) for small ratios of maximum particle displacement to bed 

 roughness . 



For waves on flowing water, the measured wavelength agreed less 

 with a theoretical value obtained by considering an equivalent uniform 

 current. However, the amplitude variation as the waves propagated onto 

 the current was in reasonable agreement with theory. 



The wave attenuation on the uniform current was measured and found 

 to be greatest per unit distance for opposing currents. This result is 

 to be expected, since the wave energy is propagating more slowly. The 

 velocity measurements with the strong following current indicated that 

 there was little phase displacement between the free-surface profile and 

 the horizontal velocity component. There was also a reduction of mean 

 velocity in the presence of waves. However, changes in mean water 

 level are not recorded, so it is difficult to judge the full effect of 

 what appears to be increased bed shear. 



Coastal Engineering Significance . Careful measurements of the type 

 presented here are necessary, yet have rarely been performed. The 

 comparisons with theory are particularly helpful since they give an 

 indication of the adequacy of those theories. This is especially true 

 for any work which involves turbulent flow. The strong influence of the 

 wave motion on the mean current profile is a striking feature which 

 should be studied in the context of the whole flume system. It is 

 ironic that even more detailed measurements of a similar system will 

 soon be published (Kemp and Simons, in preparation, 1983). 



7. CHRISTOFFERSEN, J.B., and JONSSON, I.G., "A Note on Wave Action 

 Conservation in a Dissipative Current Wave Motion," Applied Ocean 

 Research, Southhampton, England, Vol. 2, No. 4, Oct. 1980, pp. 179- 

 182. 



Keywords. Bottom Friction; Conservation Equations; Current Depth 

 Refraction; Currents, Large-Scale; Theory; Theory, Ray; Wave Action; 

 Wave Dissipation; Wave Height. 



Discussion. Refraction of steady, slowly varying water waves 

 propagating on a steady current over a gently sloping seabed are 

 studied. Dissipation due to bed friction is rigorously incorporated. 



The energy equation for the fluctuating motion is formulated in 

 terms of wave action, namely, wave energy divided by relative angular 

 frequency. This results in the classical wave action conservation 

 equation for nondissipat ive flow, supplemented by a dissipative term, 

 which is strikingly similar to wave action itself. It is simply the 

 total dissipation minus the effect of the current acting on the total 

 mean bed shear stress, divided by the relative frequency. Thus, it is 



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