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water surface level is not changed by any of the circulation within the model, mathematically
ETA(1,J) = 0 J = 1, N
(4.38)
This condition necessitates that the offshore boundary be sufficiently far from any set-up or
set-down. Other possible offshore conditions are a no-flow condition or a radiation condition.
The no flow condition would conserve water within the computational domain so that the
volume of water involved in set- up would be compensated by an equal volume of set-down
offshore. In an open ocean environment the open ocean can be conceived of as an infinite
reservoir. However in modeling laboratory experiments a no flow condition as the offshore
boundary condition would be the most appropriate. A radiation boundary condition as
proposed by Butler and Sheng (1984) imposes the condition
dr) dr)
- + C - = 0
dt dx
(4.39)
This condition allows long waves to freely propagate out of the computational domain
without any reflection. This tends to eliminate any seiche within the computational domain
which is induced by the start-up transients. This condition was applied at one time in the
present model but it did not preserve the offshore zero set-up condition and was changed in
favor of the more rigid zero water surface elevation condition. If the model is adapted for
use with time varying wave trains (an adaptation that the model can easily accommodate)
then the radiation condition will become imperative.
At the shoreline the boundary condition is that there is no flow into or out of the beach.
Since the model allows for flooding of the beach the index of the shoreline changes. The
model allows for differential flooding along the shoreline, for example, due to differences of
wave intensity in the lee of structures. For each grid column in the y direction the last grid
is the IWET(J) grid, where IWET(J) is allowed to change with changes of the mean water
level. The numerical statement of the no flow boundary condition at the shoreline is
t/(IWET(J)+l,J) = 0
J=1,N
(4.40)