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SHEAR, and LATMDC compute the radiation stresses, the bottom shear stress, and the
lateral mixing coefficients. These terms are the forcing terms in the equations of motion
and are used in the subroutine CIRC, which is the circulation model, to solve for fj, U and V.
There is a decision tree which directs the program to the three subroutines WAVE, SHEAR,
and LATMIX at selected intervals. This is purely arbitrary and is done in the interest of
computer speed. It is assumed that the forcing terms do not change at a great rate and can
thus be updated periodically. This updating is more frequent during the start-up time while
the offshore incident wave height is being increased. The CHECK subroutine is to check the
model for convergence. Since steady state conditions are assumed, this subroutine indicates
convergence when the absolute value of the percentage difference between the updated values
of U,V, and fj and the previous values is less than an arbitrarily small specified value. The
UPDATE subroutine simply updates the values of the unknowns for the next iteration. The
FLOOD subroutine allows for the addition or elimination of grid rows at the shoreline to
allow for beach flooding due to set-up.
Figure 1.3 is a flow chart of the circulation model. The subroutines XCOEF and
YCOEF determine the coefficients of the tridiagonal matrix equation for the general cases
in the x and y directions. The subroutine TRIDA solves the tridiagonal matrix equation
using the double-elimination scheme described by Carnahan, Luther, and Wilkes (1969).
Subroutines XCOJ1 and XCOJN are adaptations of XCOEF to determine the coefficients
of the tridiagonal matrix for the special case along the lateral boundary where J=1 or
J=N. Likewise YCOIM is an adaptation of YCOEF for the I=M grid row which borders
the shoreline. These adaptations are necessary because boundary conditions necessitate
different numerical formulation of some of the derivative terms. Similarly with the presence
of an emerged impermeable barrier bordering the shore side of the JJJ grid row, special
subroutines YCJJJ and YCJJJ1 are used on the grid rows I=JJJ and I=JJJ+1 so as to
properly include the boundary conditions for these grid rows, and for shore perpendicular
groins subroutines XCJGR and XCJGR1 incorporate the boundary conditions for a groin