58
This boundary condition is used in other models, though not all models allow for differential
flooding of the shoreline. Yan (1987), whose model was used to investigate waves and
currents around a tidal or fluvial discharge, used the no flow condition away from the
discharge and defined £f(IWET(J)+l,J) as equal to the discharge per grid divided by the
water depth at the grids where discharge occurred.
Other conditions are also imposed at the shoreline boundary. These are that the wave
height and the longshore velocity are both zero. These conditions are imposed at the
shoreward grid edge of the IWET(J) grids even though the wave height and longshore
velocities are specified a half grid space form the shoreline. This is done by writing x
derivatives of the radiation stress terms and of the V velocities that need to be positioned
at the center of the IWET(J) grid in terms of three points. The three points are at the
IWET(J)-1 and IWET(J) grids and the zero value at the shoreline at the edge of the
IWET(J) grid.
For the lateral boundary conditions several alternatives are available. Birkemeier and
Dalrymple (1976) and Ebersole and Dairymple (1979) both used a periodic or repeating
beach. This meant that computations were performed between the second and N grid,
and values outside of the computational domain are determined according to
Q(I,1) = Q(I,N) (4.41)
Q{I,N + 1) = <5(7,2) for all I (4.42)
for any quantity Q.
At one point this was used in the present model until the problem of what should have
been transient edge waves generated by wave obstructions during the start-up were found
to be trapped in the model. The periodic boundary condition allowed for disturbances
propagating out of the domain at one lateral boundary to enter the domain at the other
boundary. For straight and parallel contours, the periodic beach condition worked well in
the present model but with the presence of breakwaters another condition had to be used.
For the lateral boundary conditions there are two choices, either closed or open bound-