1967 
SSS eS S> 1968 ACTUAL 
—— -—— 1968) /PREDICTED 
BREAKWATER 
PLANFORMS 
CALCULATED 
—40 —30 —20 -10 0 10 20 20 40 50 60 70 80 90 
x100 FT 
Figure 29. Computed data versus actual data. 
form. This could be done in a heuristic manner, either in the global approxi- 
mation described previously or in the use of the constant depth theory of Penny 
and Price (1952). It could also be done in a more rigorous manner which would 
include the effects of a sloping beach. Thus, quantitative predictions of the 
shoreline can, in theory, be attempted in situations where onshore-offshore 
transport of sand is either negligible or is known from other sources. 
The resulting theory is presented in two equivalent forms, one in terms of 
the behavior of the shoreline y(x,t) alone, the other expressed explicitly in 
the longshore transport Q(x,t) and implicitly in y(x,t). The former has the 
advantage that numerical schemes, such as that of Crank-Nicolson can qualita- 
tively indicate the behavior of the shoreline in regions of rapid change. How- 
ever, the conservation of mass is difficult, if not initially impossible to 
achieve since any approximation of a transport-derived term (i.e., a term 
arising from 3Q/3x) will alter the transport balance. The later form allows 
the use of analytical or numerical approximations in the transport equation 
which will not disturb the total sand content of the system, but only its 
local distribution. 
The most severe and unavoidable limitations to the engineering application 
of these methods are the use of the statistical wave summaries. One possible 
use of these statistics was shown; however, many others are possible. Efficient 
and accurate use of the offshore wave statistics is endemic to the problem of 
large-scale shoreline prediction, and must be achieved before any theory (whether 
one line, multiple lines, or grid) can successfully produce accurate results. 
The problem of shoreline evolution sensitivity to time step in the input 
wave climatology would require further research. Despite this limitation, if 
the effects of wave refraction, wave diffraction, and change of lake level are 
taken into account (as in this report), and if the method is generalized, then 
a mathematical model with multiple bottom contour lines could be formulated 
which would (if the problem of wave statistics input is solved) permit a cal- 
culation of the evolution of the complete bottom topography. 
60 
