The second part of Equation 19 is
1
I 2 = ⌠ α ~η2ds
a$
(38)
⌡B 2
where B denotes all the coastline and internal land
boundaries.
j
p
Along a segment p of the coastal boundaries B
Model Domain
i
(Figure 4), the wave surface elevation function η and
$
ModelM
the variable ~ are approximated by linear functions as
a
before:
ηp = N ip ηip + N p ηp
(39)
$
$
$
j j
Figure 4. Boundary segments
~ p = Np~p + Np~ p
(40)
a
i ai
j aj
Here, we assume that i → j is the positive direction of the boundary, counter-clockwise
for the coastline boundaries and clockwise for internal land boundaries.
$
()(
)
2
2
= N p ηp + N p ηp
ηP
$
$
$
i i
j j
(N )
( N N )η
P2
(41)
P
P
P
$
= {η , η }
i
i
j
i
P
P
$$
( N N ) ( N ) η
i
j
P2
P
$
P
P
j
j
i
j
Equation 38 can then be written as
19
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