109 



destabilization forces. The dominant destabilization forces are due to the 

 combined effects of gravity and due either to offshore directed flows in 

 water depths greater than breaking or due to wave breaking in the shallower 

 depths. Fig. 7.10 presents the general situation. 



The constructive effects include the shoreward predominance in bottom 

 shear stress due to nonlinear waves. The oscillatory bottom water particle 

 velocity, u, associated with a nonlinear wave can be expressed as 



u = aicosa + a2Cos2a + ... (7.18) 



in which a is the phase angle and the a^^ are velocity amplitude 

 coefficients. Even though the time averaged bottom velocity is zero 

 (u = 0), the net onshore shear stress, t, is positive (i.e., shoreward) 

 since 



r = |£ |u|u (7.19) 



where p is the mass density of water and f is the Darcy-Weisbach fraction 

 factor. Fig. 7.11 is based on stream function (nonlinear) wave theory and 

 presents the average nondimensional shoreward shear stress, t', 



T ■ = lulu 



(7.20) 



(H/T^) 



as a function of relative water depth, h/LQ and wave steepness, H/Lq. 



7.4 RESEARCH NEEDS 



It is clear that the development of an adequate capability to predict 

 shoreline response to future sea level rise rates will require a 

 consideration of cross -shore sediment transport fundamentals and 

 applications, and a quantitative understanding of the transport components. 

 The Bruun Rule, while a good first model, is deficient in not allowing for 

 the onshore transport of sand that is clearly occurring at some locations 

 and undoubtedly occurring at many less evident locations. The three types 



