where 



H b = breaking wave height in presence of return flow 

 Cg b = group speed of waves at breaking in presence of return flow 



U b = magnitude of the return flow in the vicinity of the break point 

 Assuming C gb ~ C gb , Equation 87 can be expressed as: 



» 



H b j 



U b 

 1 - — 



c 



(88) 



gb 



Under the stated assumptions, Equation 88 demonstrates that a return flow pro- 

 duces higher breaking wave heights than if the flow is absent. Figure 44a and 

 b shows fit as a function of deepwater wave steepness for seaward angles of 5 

 and 20 deg. The highest fi b -values result from conditions in which the 

 cross -sectional water area shoreward of the bar was small (/3 3 = deg) or the 

 shoreward angle was very steep (/3 3 = 40 deg) . Return flow increases for 

 /3 3 = deg because of continuity; i.e., velocity increases if the water area 

 shoreward of the bar decreases. For situations with steep shoreward slopes, 

 the vertical component of return flow velocity is directed opposite (up) to 

 that expected for a plane slope (down) . For cases in which the weir flow was 

 observed, steep /Si-angles and low wave steepness, the return flow speed in- 

 creased over the crest of the bar. Equation 88 shows that under these circum- 

 stances H b will increase, which may explain the increase in Ob— values for 

 20— deg angles at low values of wave steepness in Figures 42 and 43. 



143. The preceding derivation shows that a stronger return flow 

 increases the breaker height, but observations indicate ^ i- s still well 

 behaved in the presence of strong return flow, unlike the breaker depth index. 

 This suggests breaker height is a more stable parameter than breaker depth for 

 situations with steep bar faces. The derivation can be refined by including 

 the wave-current interaction term S xx dU/dx and actual values of (C g ) b and 

 (C g ) b , leading to an equation that must be solved by iteration. 



97 



