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reflective conditions are imposed at the barrier by assuming that the derivatives of any
property perpendicular to the breakwater has a zero value at the breakwater.
In the circulation model the interned boundary condition of impermeability at the bar
rier is imposed by setting the velocity component normal to the barrier equal to zero.
V(I,Jbrk+i) = 0 for all I > Ibrk (5.12)
To insure that current-induced momentum is not diffused across the barrier, subroutines
were introduced in the computation for the x sweep for the two grid columns adjacent to
the barrier.
Two sample cases were run for comparison purposes. The first case is a breakwater
extending 400 meters from the shoreline on a beach with a composite slope of 1 on 10 for
the first one hundred meters and a slope of 1 on 100 beyond that point. This is a geometry
selected by Liu and Mei (1975). A deep water wave height of 1 meter and a deep water
wave angle of 45 degrees was used by Liu and Mei. Using linear shoaling and refraction
this gives a wave height of .84 meters and a wave angle of 31.15 degrees as the wave input
conditions at the offshore grid row 800 meters from shore in a depth of 16.95 meters.
The solution method of Liu and Mei was to solve for the wave field in the absence of
currents and mean water level changes and then use the wave field as a constant forcing in the
solution of the circulation. By ignoring the lateral mixing and advective acceleration terms
and assuming steady state conditions, and by expressing the two horizontal components of
the depth integrated flow as derivatives of a stream function ip, the two horizontal equations
of motion were reduced to one Poisson equation
vV = /(*,y) (5.13)
where the / term contains the forcing due to water level gradients, friction and wave forcing.
This equation represents a boundary value problem with two unknowns ip and fj. Upon
specifying boundary values an initial guess for the water surface fj is made and then Eq. 5.13
is solved for ip. With this new solution for ip the value of rj is updated by solving steady