Figure 25. Schematic of wave and longshore current velocity vectors in bed 

 shear-stress models. 



(1) Strong Currents at Small Angles . Following the earlier work 

 of Jonsson (1966a) '^'' for waves and currents in the same direction, Jonsson, 

 Skovgaard, and Jacobsen (1974) proposed a simple interpolation formula for 

 the instantaneous friction factor f when the waves are roughly normal to 

 the current direction (i.e., a = m Fig. 25). 



f = f 



CW V 



+ (f - f )siny 



(75) 



This made f identical to the wave friction factor fw with no current (y = 

 0°) and also made f equal to the current friction factor f with no waves 

 present (y = 90°). The combined friction factor f^^ is time dependent, since 

 Ut, varies over the wave period. Using linear wave theory for Ut., Jc^^json, 

 Skovgaard, and Jacobsen (1974) derived the following expression using equa- 

 tion (75) in equation (52) 



^By 



= f^-aP 



kn-2 



(76) 



for the time- averaged bottom shear stress parallel to the coast. The time- 

 averaged friction coefficient f is found from 

 ^ s 



^-^ JONSSON, I.G., "The Friction Factor for a Current Superimposed by Waves 

 Basic Research Program, Report 11, 2-12, ISVA, Technical University, 

 Denmark, 1966a (not in bibliography). 



93 



