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information meaning among other things that y variations of the wave field are contained
within the complex amplitude. The term parabolic equation indicates that there are
first order derivatives in the x direction and second order derivatives in the y direction.
The method of solution is to solve for the amplitude on the 1+1 grid row in terms of the
known amplitude values on the I grid row. The solution scheme starts on the first grid row
using the prescribed offshore incident wave and then advances grid row by grid row to the
last grid row. To advance to the next grid row the amplitude values on the 1+1 grid row
are implicitly formulated using a Crank-Nicolson scheme. This will be further discussed in
section 4.2 which describes the finite-differencing scheme for the parabolic wave equation.
Once the complex amplitudes are known the radiation stress terms are computed in terms
of the absolute value of the amplitude and the gradients of the amplitude. This is described
in section 2.2.
The circulation model and the wave model are the heart of the program; however there
is much more. In all there are some 27 subroutines in the program. These subroutines cover
everything from input and output to convergence checks and flooding of the shoreline. The
main program is compartmentalized into many subroutines so as to facilitate any changes
or future upgrading. For example, the bottom shear stress, a term of importance in the
equations of motion, currently uses a crude approximation. If a better approximation is
developed that is also computationally efficient, it will be an easy task to replace the present
subroutine that computes the bottom shear with the newer subroutine. There are many
places where the model can be improved with better assumptions and better approxima
tions. These will be discussed in detail in the final chapter outlining recommendations for
further study. The modular construction of the model also allows for ease in substituting
one wave model for another.
Figure 1.2 shows a flow chart of the computer program. The subroutine INPUT is called
to initialize the values of the unknowns and to input the water depth, the offshore wave
height and direction and the position of any structures. The three subroutines WAVE,