y(x,0) = 



(30) 



These conditions may represent an excavation or a natural embayment of rec- 

 tangular shape. Walton and Chiu (1979) present the following solution: 



y(x,t) = 2 y Q 



erf c 



2_IJE\ + erfc /iii\ 

 2/ e t / \2/ e t / 



(31) 



for t > and -« < x < oo . 



This- solution may be obtained by superimposing Equation 16 with a negative 

 sign on a beach of width y . In general, with due regard to the boundary 

 and initial conditions, it is possible to derive new solutions simply by 

 superimposing existing solutions since the governing differential equation 

 (Equation 9) is linear. Equation 31 is symmetric with respect to the y-axis, 

 and only half of the solution region is illustrated in Figure 11. 



0.5 1 1.5 2 



RL0NGSH0RE DISTANCE (x/o) 



Figure 11. Shoreline evolution of a rectangular cut in an 

 infinite beach of width y 



25 



