energy equation is given. (it should be noted that Inraan and Bowen 

 (1962) missed the just - mentioned correction term in their analysis.) 

 The dissipation per unit area is assumed to be the product of instan- 

 taneous bed shear and corresponding particle velocity. 



Also the energy equation results in an expression which determines 

 the current friction factor, knowing wave height gradient and mean water 

 surface slope. Eliminating either of these two quantities from the two 

 conservation equations results in two expressions for the current wave 

 friction factor, which again determines the current friction factor 

 through a factor containing the ratio between current velocity and 

 maximum wave particle velocity at the bed. 



Measuring the slope of the mean water surface is difficult*, how- 

 ever, measurements of the decrement of wave height have been performed 

 by Inman and Bowen (1962), in a wave flume with a rippled bed, and with 

 currents in the direction of wave travel of up to 6 centimeters per 

 second. A run with waves of period 1.4 seconds, wave height 15.4 centi- 

 meters and water depth 50.3 centimeters is analyzed. 



For no current the wave friction factor is 0.30 and the current 

 wave friction factor (i.e., the factor giving the instantaneous bed shear 

 from total bed velocity squared) was almost constant, ranging from 0.26 

 to 0.31, i.e., close to the wave friction factor. This is expected, 

 since current velocity over maximum wave particle velocity at the bed is 

 small, at maximum about 0.28. 



A further result of the analysis is that "large waves" (wave par- 

 ticle velocity much larger than the current velocity) produce a current 

 friction factor (i.e., the factor giving the mean bed shear stress from 

 mean velocity squared) which is larger — by order of magnitude — than 

 the friction factor for a pure current. In the experiments the friction 

 velocity was, in fact, of the order of magnitude of the current velo- 

 city. So the superposition of the waves on the current drastically 

 increased the mean bed shear stress, as expected. 



A simple interpolation formula for the current wave friction factor 

 is introduced, giving rather good agreement with the experiments that 

 predict mean bed shear stress. It should be observed, though, that 

 since the current velocities in these experiments are quite weak, this 

 agreement does not really verify the interpolation chosen. Rather it 

 indicates that the idea of a constant friction factor on the 

 instantaneous velocity squared is reasonable when calculating the 

 instantaneous shear stress. (The interpolation formula has later been 

 used with some success by Brevik (1980) and BREVIK and AAS (1980).) 



In the present adaptation of the Inraan and Bowen (1962) data there 

 is a small error, since wave phase speed etc. is calculated without 

 correction for the "Doppler shift." Because of the small current 

 velocities, however, the maximum error on the wavelength is only about 3 

 percent . 



30 



