Chemistry Reference
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(where
ȖE
is the three source terms that are linear in
E
taken together),
starting from some point
k
0
in the spectrum with boundary value
E
(
k
0
), to-
wards higher wave numbers. At the lower wave numbers and the bound-
ary, i.e. at
k
d , a JONSWAP-type spectrum is assumed. The exact
value of
k
0
depends on wind speed, but is around 80 rad m
-1
. The saturation
level in the gravity range is taken as
k
0
B
(
k
)
D
/
2
, with 'Phillips con-
Ph
stant'
D
Ph
0
24
F
1
a function of wave age
Ȥ
. The wave age is in turn de-
fined as
F
u
/
*
c
, with
c
p
the phase speed at the JONSWAP peak.
p
2.2 Low wave number extension to the VIERS-1 spectrum
The gravity region is not physically modelled in the VIERS-1 spectrum.
As mentioned above, a JONSWAP spectrum is assumed there, which im-
plies a
k
-4
saturation behaviour with a long wave cut-off (plus an en-
hancement of the spectral peak). The gravity region is, however, relevant
for the modelling of the radar backscatter of slick-covered sea surface, di-
rectly via Bragg scattering when using longer radar wavelengths (order 10
cm or longer), or through tilt modulation by the longer waves that affects
all radar wavelengths. Furthermore, in the next section it will be tried to
derive relaxation rates, and for that a modelling of the spectrum is also
needed. Therefore, it was attempted to extend the equilibrium spectral
model into the saturation region, i.e. between the spectral peak and the
gravity/capillary transition range, in a relatively simple and crude way.
The shape of the gravity wave spectrum in the saturation range has been
debated in the literature (e.g., Kitaigorodskii 1983; Phillips 1985; Apel
1994). Arguments favour a flat curvature spectrum
B
(
k
), or a curvature
spectrum of the form
0
B
v (in the absence of slicks). As the most
recent equilibrium spectra from the literature (Apel 1994; Romeiser et al.
1997) seem to favour a flat curvature spectrum, we can adhere to the origi-
nal VIERS approach which also takes on a flat curvature spectrum in the
saturation range, as noted above. The VIERS approach will furthermore be
followed by retaining the description of the non-linear interaction as in Eq.
9, and letting the 3-wave interaction coefficient go to zero in the saturation
range. (In the original VIERS-1 modelling, this coefficient is already
halved at
k
0
.) In the saturation range, then, in the absence of slicks, we are
left with the energy balance (the viscous dissipation being small enough to
neglect here):
(
)
k
u
1
S
(
E
)
GZ
(
*
)
2
E
E
(
E
)
kE
'
0
(12)
k
c
