60
o
Figure 4.2: Start-up function according to Eq. 4.43 with Ci=30 and Ci=3.
the wave model which is contrary to the condition in the circulation model can introduce
instabilities in the overall model. The interaction of the two models is more sensitive than
either of the models individually.
The C(t) term in equation 4.43 is a start-up function which smoothly goes from zero
to unity so as to bring the incident wave height from zero to H0 and minimize any shock
loading of the model. Mathematically it is given by
C(t) = .5
t
1 + tanh( Ci)
w
(4.45)
where C\ and Ci are arbitrary constants to adjust the slope and offset of the curve. Fig
ure 4.2 shows equation 4.45 for C\ and Ci equal to 30 and 3 respectively.
The lateral boundary conditions are either open or reflective. The reflective condition
is expressed as
(4.46)
while the open condition is expressed as
ai =,mA <4-47)
where m is the longshore component of the wavenumber which in the absence of diffraction
effects remains constant
m = k0 sin 90 = k sin 9
(4.48)