For the problem under consideration, long-term evolution is of primary 
importance, the short-term evolution appearing as a superimposed perturbation 
on the general beach profile. Evolution of the coastline is characterized by 
low monotone variations or trends on which are superimposed short bursts of 
rapid development associated with storms. 
The primary cause of long-term evolution is water waves or wave-generated 
currents. Three phenomena intervene in the action which waves have on shore- 
line evolution: 
(a) Erosion of beach material by short-period seas versus accre- 
tion by longer period swells; 
(b) effect of water level changes on erosion; and 
(c) effect of breakwaters, groins, and other structures. 
Although mathematical modeling of shoreline evolution has inspired some 
research, it has received only limited attention from practicing engineers. 
The present methodology is based mainly on (a) the local experience of engi- 
neers who have a knowledge of their sectors, understand littoral processes, 
and have an inherent intuition of what should happen; and (b) movable-bed 
scale models that require extensive field data for their calibration. 
In the past, theorists have been dealing with idealized situations, rarely 
encountered in engineering practice. Mathematical modelers apparently have 
long been discouraged by the inherent complexity of the phenomena encountered 
in coastal morphology. The lack of well-accepted laws of sediment transport, 
offshore-onshore movement, and poor wave climate statistics have made the 
task of calibrating mathematical models very difficult. Considering the im- 
portance of determining the effect of construction of long groins and naviga- 
tion structures, and the progress made in determining wave climate and littoral 
drift, a mathematical approach now appears feasible. 
The complexity of beach phenomena could, to a large extent, be taken into 
account by a numerical mathematical scheme (instead of closed-form solutions), 
dividing space and time intervals into small elements in which the inherent 
complexity of the morphology could be taken into account. Furthermore, better 
knowledge of the wave climate, a necessary input, will allow a better calibra- 
tion of coastal constants (such as those in the littoral drift formula). 
In past investigations (Le Mehaute and Soldate, 1977), many important ef- 
fects have been neglected, such as combined effects of wave diffraction around 
littoral obstacles, change of sea level, height of berm and bluff, beach slope, 
etc. The present investigation attempts to include all the important factors 
associated with long-term shoreline evolution. In the case of the Great Lakes, 
importance must be given to variations in lake level. The coastal zone is de- 
fined by a three-dimensional bottom topography instead of a two-dimensional 
shoreline (or two lines) as in the previous cases. 
Mathematical modeling is essentially approached by: 
(a) Understanding the phenomenology of shoreline evolution 
quantitatively. 
