106 



7.3.1 Kinematic (Sediment Budget) Considerations 



The change in absolute elevation, z, of the sediment-water interface 

 at a horizontal point (x,y) can be expressed in terms of the sediment 

 transport components, q^^ and qy and any source terms, 



az=_(!%c + % + s (7.9) 



at 3x dy 



For reference purposes , the x and y coordinates are selected in the 

 offshore and alongshore directions, respectively such that qy represents 

 the local longshore component of sediment transport. The formal origin of 

 the Bruun Rule can be demonstrated by assuming that there are no sources 

 (s = 0) , that there are no gradients in longshore sediment transport Sqy/Sy 

 = 0, and integrating the resulting equation from x]^ to X2 , 



/2|^dx = -X'2|S^dx = q,^-q.2 (7.10) 



XI XI 



and if q^^ and q^^, are sufficiently landward and seaward that no motion 

 occurs , q^^ = qx-i = . resulting in 



;^ S dx = (7.11) 



""x^ 3t 



We now decompose z into two components, one due to the uniform vertical 

 profile displacement, 7.\, and the second to the uniform horizontal 

 displacement Z2(x), that is. 



