Geoscience Reference
In-Depth Information
Combi spectrum
(7.46)
with
U
10
/
c
p
=
2
.
7 and
U
10
=
10m
/
s. Away from the peak
f
p
,
the distance between directional maxima
θ
p
was lineally increased.
A distinct trough in the dissipation
S
ds
(
f
,θ)
is visible in the main direction of the
0
◦
. At the upper frequency
f
max
, the source-function peaks are
located symmetrically to the main propagation direction at angles
wave propagation at
θ
=
30
o
. Thus, the
parameters of the directional function
(7.56)
allow us to vary the initial shape of the three-
dimensional dissipation function
S
ds
(
θ
p
=±
f
,θ)
which is then allowed to evolve in the course of
wave propagation.
As mentioned above in this section, based on the constraints
(7.38)
and
(7.47)
,primary
calibrations of the wind-input and dissipation functions can be done separately, and if the
constraints describe the behaviour of the source functions comprehensively, no further tun-
ing would be required based on the evolution tests. The evolution curves, of course, have to
be satisfied in any case. This way they become verification, rather than tuning/calibration
means.
The integral constraints
(7.38)
and
(7.47)
, however, cannot attend to details of the spec-
tral behaviour of the source functions, and further modifications in this regard have proved
necessary, i.e. frequency-dependent coefficients of the inherent-dissipation level
a
1
(7.55)
and the cumulative level
a
2
(7.54)
were introduced. Once this was done, the wave-evolution
tests were performed without further tuning of the source functions, with the self-adjustment
routine active in order to satisfy the constraints at each integration step.
The evolution tests were conducted with research two-dimensional wave model WAVE-
TIME, which employs full computations of the nonlinear integral
S
nl
(
Van Vledder
,
2002
,
2006
). The latter uses the Webb-Resio-Tracy algorithm (
Webb
,
1978
;
Tracy & Resio
,
1982
). The resulting time-limited evolution of integral, spectral and directional wave prop-
erties demonstrated good agreement of the simulated evolution with known experimental
dependences (see
Babanin
et al.
,
2010c
).
For direct comparisons of the evolution of the newly calibrated dissipation term
S
ds
(7.50)
-
(7.52)
, the only experimental data suitable to date are those obtained, based on the
dimensional argument, by means of estimating distributions of the length
of breaking
crests as described in
Sections 3.4
and
3.6
. Following this argument
(3.30)
and empirical
dependence
(3.31)
, the dissipation distribution along phase speeds
c
can be expressed as
(
c
)
10
U
10
3
c
5
g
(
S
ds
(
c
)
=
b
br
ρ
w
c
)
(7.58)
(note that the quantitative empirical dependence is not dimensionally consistent).
S
ds
(
c
)
can then be converted into customary
S
ds
(
f
)
:
g
2
1
f
2
S
ds
(
S
ds
(
f
)
=
c
).
(7.59)
π
As discussed in
Sections 3.4
and
3.6
, in the case of a steady breaker,
b
br
in
(7.58)
is sim-
ply a proportionality coefficient. However, in the field the breaking is principally unsteady.
Measurements within realistic unsteady-breaking conditions in the laboratory and the field
Search WWH ::
Custom Search