MATHEMATICAL MODELING OF SHORELINE EVOLUTION 



by 



Bernard Le Mehaute and Mills Soldate 



I. INTRODUCTION 



This interim report presents a critical literature survey on the 

 subject of mathematical modeling of shoreline evolution. Hopefully, 

 this review will lead the way in establishing a flexible and practical 

 numerical method suitable to predict shoreline evolution, resulting 

 from the construction of navigation and shore protection structures in 

 the Great Lakes. 



To focus attention on the most pertinent literature, the subject 

 under consideration is Timited to long-term shoreline evolution as 

 defined below. 



Three time scales of shoreline evolution can be distinguished: 



(a) Geological evolution taking place over centuries; 



(b) long-term evolution from year-to-year or decade; and 



(c) short-term or seasonal evolution and evolution 

 taking place during a major storm. 



Associated with these time scales are distances or ranges of influ- 

 ence over which changes occur. The geological time scale deals, for 

 instance, with the entire area of the Great Lakes. The long-term 

 evolution deals with a more limited stretch of shoreline and range of 

 influence; e.g., between two headlands or between two harbor entrances. 

 The short-term evolution deals with the intricacies of the surf zone 

 circulation; e.g., summer profile-winter profile, bar, rhythmic beach 

 patterns, etc. 



For the problem under consideration, long-term evolution is of pri- 

 mary importance, the short-term evolution appearing as a superimposed per- 

 turbation on the general beach profile. Evolution of the coastline is 

 characterized by low monotone variations or trends on which are super- 

 imposed 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 shoreline evolution: 



(a) Erosion of beach material by short period seas versus 

 accretion by longer period swells; 



