Chemistry Reference
In-Depth Information
In order to further assess the values of the relaxation rate found here, we
compare them with Plant and Wright's (1977) parameterisation which is
often used. (Other parameterisations are roughly similar, but can deviate
by factors of up to 4.) The comparison is plotted in Fig. 5. It can be seen
that in the saturation/gravity range and in the far capillary range, the values
found here are quite realistic. Only in the intermediate range, where the
negative
ȝ
-values are found, is a significant deviation present.
Fig. 5.
Computed relaxation rates (discontinued curves) compared to Plant and
Wright relaxation rates (continuous curves) on a logarithmic scale, for wind
speeds
U
10
= 5 m/s (drawn) and 10 m/s (dotted). Clean surface
The fact that in the saturation range the computed relaxation rate is real-
istic, means that the choice of
p
1
=
p
2
= 1 in Eqs. 15, 18 appears to be justi-
fied. The values of
p
1
and
p
2
determine to which of the coefficients
f
1
, f
2
or
f
3
the breaking terms
S
sd
(that were introduced, Eq. 15, to force a flat satu-
ration spectrum) contribute, thereby directly influencing
ȝ
.
As a last check to assess the validity of the method used, it is applied to
Phillips' (1985) saturation spectrum. In Phillips' effort to derive a satura-
tion spectrum (in his case
0
B
v ), he defines forms for three source
terms in the energy balance equation,
viz.
wind input, non-linear inter-
action and dissipation. When written in the form of Eq. 21, his energy bal-
ance has
f
2
= 0. In that case, Eq. 24 can actually be further reduced to
1
(
)
k
P
2
f
. Save for a factor of 2, this yields the Plant and Wright relaxation
