16 



water surface (77) 



MWL {z = 0) 



Figure 2.1: Coordinate system used for the two dimensional method 



Field Equation The field equation is mass conservation for irrotational flow, in 

 the form of the Laplace equation: 



2 , _ ^V d^6 



(2.2) 



Boundary Conditions The boundary conditions are the bottom boundary condi- 

 tion for a locally horizontal bed (BBC), 



w — ^— = at z — —h 

 oz 



the kinematic free surface boundary condition (KFSBC), 



dr] dr] 



at ox 



at z = T] 



and the dynamic free surface boundary condition (DFSBC), 



-^ + -u^ + -w^ + 9r]-B = at 2 = 77 



(2.3) 



(2.4) 



(2.5) 



where r) is the elevation of the free surface, g is the acceleration of gravity, and B is 

 the Bernoulli constant. 



The kinematic free surface boundary condition (Eq. 2.4) includes both the time 

 and spatial gradients of the water surface. When working with a subsurface gauge. 



