Geoscience Reference
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2.1 Breaking onset
Figure 1.2
demonstrates an incipient wave breaker modelled by means of a CS model (solid
line). Visually and intuitively, the shape of the breaker appears quite realistic, and therefore
it is instructive to review the model's definition of breaking onset. A numerical model
cannot operate by means of phenomenological definitions, and obviously the inception of
breaking had to be explicitly defined in mathematical terms.
In numerical simulations, a wave is regarded as breaking if the water surface becomes
vertical at any point (
Babanin
et al.
,
2007a
,
2009a
,
2010a
). The criterion for terminating
the model run was defined by the first appearance of a non-single value of surface in the
interval
x
=
(
0
,
L
)
:
x
(
i
+
1
)<
x
(
i
),
i
=
1
,
2
,
3
...,
N
−
1
,
(2.1)
where
N
is the number of points on the wave profile over its length
L
.
This definition is further illustrated in
Figure 2.1
, also simulated by means of the CS
model. Here, development of a very steep harmonic wave with initial steepness
=
ak
=
0
corresponds to
the wave period). This is effectively a rapidly developing breaker, as in the two-dimensional
CS model such waves break within one period.
The model has obvious limitations in simulating the final stages of incipient breaking
and was stopped when the water surface became vertical at any point. Strictly speaking, this
geometrical property of the surface can be used as a physical definition of breaking onset.
In numerical simulations it was noticed that local steepness can be very large, but the carrier
wave can still recover to a non-breaking state. If, however, a negative slope appears locally,
the wave never returns to a non-breaking scenario because the water volume intersecting
the vertical line tends to collapse. That is, after the moment when criterion
(2.1)
has been
reached, the solution never returns to stability: the volume of fluid crossing the vertical
x
.
32, is shown in terms of dimensionless time (in the horizontal scale, 2
π
(
i
)
Figure 2.1 Numerical simulation of a steep wave evolving towards breaking, as predicted by the CS
model. The wave propagates from left to right. Chalikov (2007, personal communication)
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