ANALYTICAL SOLUTIONS OF THE ONE-LINE MODEL 

 OF SHORELINE CHANGE 



PART I: INTRODUCTION 

 Background 



1. Mathematical modeling of shoreline change has proven to be a useful 

 engineering technique for understanding and predicting the evolution of the 

 plan shape of sandy beaches. In particular, mathematical models provide a 

 concise, quantitative means of describing systematic trends in shoreline evo- 

 lution commonly observed at groins, jetties, and detached breakwaters and 

 produced by coastal engineering activities such as beach nourishment and sand 

 mining. 



2. Qualitative and quantitative understanding of idealized shoreline 

 response to the governing processes is necessary in investigations of beach 

 behavior. By developing analytical or closed-form solutions originating from 

 mathematical models which describe the basic physics involved to a satisfac- 

 tory level of accuracy, essential features of beach response may be derived, 

 isolated, and more readily comprehended than in complex approaches such as 

 numerical and physical modeling. Also, with an analytical solution as a 

 starting point, it is possible to estimate, rapidly and economically, charac- 

 teristic quantities associated with the phenomenon, such as the time elapsed 

 before bypassing of a groin occurs, percentage of volume lost from a beach 

 fill, and growth of a salient (emerging tombolo) behind a detached breakwater. 

 Another useful property is the capability to obtain equilibrium conditions 

 from asymptotic solutions. Closed-form solutions for shoreline change can 

 also be used as a teaching aid. However, the complexity of beach change 

 implies that results obtained from a model should be interpreted with care and 

 with awareness of the underlying assumptions. Closed-form mathematical models 

 cannot be expected to provide quantitatively accurate solutions to problems 

 involving complex boundary conditions and wave inputs. In engineering design, 

 a numerical model of shoreline evolution would be more appropriate. 



3. The equations describing shoreline evolution fast become excessively 

 complicated to permit analytical treatment if too many phenomena are described 



