Table 1. u versus (u) . 



u 0.1 0.2 0.3 0.4 0.5 0.7 0.9 1.2 2 



i(u) 0.112 0.223 0.328 0.428 0.520 0.667 0.796 0.910 0.995 1 



Fig. 2 illustrates the shoreline evolution as defined by equation (8). 

 It is interesting that these curves are homothetic with respect to the 

 origin o ; i.e., 



oA = oB_ = oC_ g^^ 

 oA' oB' oC ' 



The horizontal lengths grow with t , and in particular, 



tan a 



oy = 2 VkT • 



A tangent to the shoreline at the groin intersects the initial shoreline 



defined by y = o at a point a distance of 2 VKt/ir updrift from 

 the groin. 



The ratio of the area of sand accumulation, such as is in oyx , to 



D 



the area of sand contained in the triangular fillet, oyx , is 1.56 and 

 the distance ox h. 2 . 7 ox . This ratio permits rapid assessment of 



the total amount of sand accumulated updrift from a single measurement 



of the angle a , and determination of D as shown in Section IV. 



'^ o 



The end of the groin of length, oy = £ , is reached when 

 2 



1 .1. . 2 

 4K tan a 



(10) 



When t _> t , the boundary conditions must be modified since the groin 

 no longer traps all the sand but bypasses some of it. 



If the same theory is applied to the beach downdrift of the groin 

 and if assumed that the wave diffraction effects are negligible, the 

 beach is eroded in a form symmetric with the updrift accretion. 



