The Wave-Induced Current Model, CURRENT 



48. When waves break and decay in the surf zone, in general they induce 

 currents in the longshore and cross-shore directions and changes in the mean 

 water level. These currents play a major role in the movement of sediment in 

 the nearshore. They are computed using the model CURRENT. 



Equations of motion 



49. The hydrodynamic equations used in the model for wave-induced 

 currents may be derived from the Navier-Stokes equations (for details, see 

 Phillips 1969 and Ebersole 1980). It is assumed in the derivation that the 

 fluid is homogeneous and incompressible, and the vertical accelerations are 

 negligible so that the pressure distribution is hydrostatic. By vertically 

 integrating the three-dimensional form of the equations and applying appropri- 

 ate boundary conditions, the depth-averaged two-dimensional form of the equa- 

 tions of motion and continuity are obtained. These equations are derived by 

 time-averaging over a time interval corresponding to the period of the waves. 

 Referring to a Cartesian coordinate scheme (Figure 8), these are: 



Momentum 



lU + U^ + V^+g^ + i-T +i- (^ + ^) - i ^ = (44) 



9t ^ 3x ay ^ 3x pd ^bx pd \ 9x 3y / p 9y ^ ^ 



lY + u^ + vi^+gl^ + ^T +1- (^ + ^^ _ i !!2EZ = (45) 



9t 9x 9y ^ 9y pd by pd \ 9x 9y / p 9x " ^^"^^ 



Continuity 



where 



li + k ("^> -^ 1^ (^^) = ^''^ 



U and V = depth-averaged horizontal velocity components at 

 time t in the x- and y-directions, 

 respectively, ft/sec 



ri = displacement of the mean free surface with 

 respect to the still-water level, ft 



3 

 p = mass density of seawater, slugs/ft 



31 



