Geoscience Reference
In-Depth Information
Then, for generality and for parameterisation purposes, it is convenient to represent the
severity in nondimensional terms as a fraction
s
of this energy which is lost to breaking:
2
E
s
(
f
)
=
s
(
f
)
E
(
f
)
=
s
(
f
)
H
(
f
)
,
(2.24)
that is
2
s
(
f
)
n
(
f
)
H
(
f
)
S
ds
(
f
)
=
.
(2.25)
t
In linear waves, the depth-integrated kinetic energy
Q
(
f
)
)
=
ρ
w
u
2
2
Q
(
f
(
f
)
+
w(
f
)
(2.26)
equals the potential energy
(2.22)
(here,
u
and
are horizontal and vertical components of
the surface orbital velocity respectively), and the total energy can easily be estimated. In
strongly nonlinear waves, this is not necessarily true and therefore
(2.22)
-
(2.25)
and further
expressions in terms of wave height
H
should be applied to wave trains measured before
and after the rapid transient processes of breaking occur. This is how experiments intended
for the measurement of breaking severity are usually designed (e.g.
Rapp &Melville
,
1990
;
Manasseh
et al.
,
2006
;
Babanin
et al.
,
2009a
,
2010a
), but to avoid ambiguity this should
be explicitly mentioned.
The severity coefficient
s
, or simply breaking severity or breaking strength hereinafter,
is often treated as a fixed fraction, for instance
w
s
=
50%
(2.27)
of the energy that a wave had before breaking (this is approximately the estimate that was
obtained, for example, in laboratory experiments by
Xu
et al.
(
1986
)). Such an estimate,
however, is not general due to four main reasons, and the resulting deviations from this
mean estimate can be enormous.
The first reason is the cause of the wave breaking, or in other words the means by
which wave breaking was achieved in the laboratory. These means are many. For example,
waves can be made to break using an artificial obstacle or a submerged shoal, and this
is a robust practical way to investigate relevant wave-breaking properties and phenomena
(e.g.
Ramberg & Bartholomew
,
1982
;
Manasseh
et al.
,
2006
;
Calabresea
et al.
,
2008
). If
natural deep-water processes leading to breaking are simulated, there is still a variety of
possibilities: superposition of linear waves achieved through use of frequency dispersion
(e.g.
Longuet-Higgins
,
1974
;
Rapp &Melville
,
1990
;
Meza
et al.
,
2000
,see
(2.18)
), super-
position of nonlinear waves through amplitude dispersion (e.g.
Donelan
,
1978
;
Pierson
et al.
,
1992
,(see
2.15
)) and evolution of nonlinear wave groups (e.g.
Melville
,
1982
;
Babanin
et al.
,
2007a
,
2009a
,
2010a
). The latter evolution to breaking may exhibit essen-
tially different characteristics in directional wave fields (
Onorato
et al.
,
2009a
,
b
;
Waseda
et al.
,
2009a
;
Babanin
et al.
,
2011a
). In the case of wind forcing, wave breaking may be
affected, and this effect is of principal significance as far as breaking strength is concerned
(
Babanin
et al.
,
2009a
,
2010a
;
Galchenko
et al.
,
2010
). Wave breaking and the severity of
short spectral waves to a large extent are caused or at least impacted by the modulations
Search WWH ::
Custom Search