Chemistry Reference
In-Depth Information
&
&
&
S
nl
(
E
(
k
))
Z
I
(
k
)
Z
I
(
k
)
(5)
3
4
with
I
3
and
I
4
the 3- and 4-wave action collision integrals (e.g., Hassel-
mann 1963 for the 4-wave interaction), it is written rather as the diver-
gence of a spectral energy flux vector (Snoeij et al. 1993):
&
&
&
&
S
nl
(
E
(
k
))
$
(
k
)
.
(6)
The spectral energy flux vector has the form
&
&
&
&
&
&
(
k
)
Z
k
I
(
k
)
Z
k
I
(
k
)
.
(7)
3
4
The collision integrals are written as
&
&
(8)
2
5
3
9
I
(
k
)
D
N
k
c
/
c
,
I
(
k
)
D
N
k
/
c
,
3
3
g
4
4
g
E
N
the wave action,
c
g
the group speed of the surface waves, and
with
Z
Į
3
,
Į
4
parameters that can in general (on dimensional grounds) be functions
of
c
/
c
g
. In the VIERS-1 model,
Į
3
goes to zero when
c
/
c
g
goes to 2 (i.e., for
pure gravity waves), and
Į
4
is taken to be constant.
In spite of the relevance of angular structure in the spectrum (e.g., Ko-
men et al. 1984), the radial dependence is integrated out, and the energy
balance is solved only as a function of
k
. After angular integration, the
non-linear source term becomes
1
S
nl
(
E
(
k
))
'
(
k
)
(9)
k
d
f
(using the notation
f
'
) and
d
k
c
4
(
k
)
Z
k
2
I
(
k
)
Z
k
2
I
(
k
)
D
B
2
(
k
)
D
B
3
(
k
)
(10)
3
4
3
4
c
g
using the 'curvature spectrum'
B
(
k
) =
k
4
F
(
k
).
This approach is similar to Kitaigorodskii's (1983), without, however,
taking
( as constant.
The resulting energy balance is solved by numerically integrating the
differential equation
)
'
(
k
)
k
J
E
(
k
)
(11)
