where a is aconstant. For the standard breakwater problem, the most logical 
choice for this constant is given by 
Z 
1 
= ———;— = |(Z cos a, cos op - Sin a, Sin a,)——77 a (55) 
eee yan aa ( Oo b O Or, BAY a 
since the shoreline in this case is principally governed by its behavior at the 
breakwater. This problem (defined by eq. 55) has the solution 
Vat 
2 
VAeent) = 2) canoe lems /4at 
V0 
K 
- tan a x erfc{— == (56) 
Gr 
which is the same as that of Penard-Considere except that the constant a has 
been changed. This problem, however, doesn't conserve mass since 
co 
3 P : 
een y(x,t) dx = z sin a cos a sin za cos a 
ae 46 
When this approximation is used in the transport equation for Q, the 
problem becomes 
3Q 2 
Ns cia 
dt ax? 
subject to the boundary conditions 
Q(x = 0) = 0 
Oise 2) GS G Sin oH, 
which has the solution 
cone 
Q(x,t) = cos a sin ap erf leas) (57) 
Integrating the equation, 
dy _ 2Q 
ot ox 
gives 
VR 2 x x 
= i Moai? (ere ene | es woPe ae 
y(X%,t) = cos o sin Oy [2 e = Sree ze) (58) 
which is of the same form as the previous solution (eq. 56). 
III. INPUT DATA 
1. Description and History of Navigation Project at Holland Harbor. 
The input data, which are pertinent only to the present investigation, deal 
exclusively with the area near Holland Harbor, Michigan (U.S. Army Engineer 
District, Detroit, 1975). Construction at Holland Harbor began about 1856 when 
the city of Holland cut through a narrow tongue of land between Lake Michigan and 
Lake Macatawa (Fig. 12). The present dimensions of the navigation project were 
established in 1909. The existing navigation structures have been constructed, 
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