Geoscience Reference
In-Depth Information
Dao
et al.
(
2010
). Based on the smoothed particle hydrodynamics method (SPH,
Lucy
,
1977
;
Monaghan
,
1977
), the water volume is treated as a set of large numbers of par-
ticles, each having its own mass and characterised by a kernel of its interactions with
neighbouring particles.
In
Tulin & Landrini
(
2001
), spline kernels of the third and fifth orders were used, which
accommodated 30 to 50 particles within interaction range of each individual particle, with
the total number of particles being up to the order of 10
5
. As the authors put it:
“Each particle moves in the force field generated by the whole particle system and the physical
quantities evolve according to suitable evolution laws following from the original differential field
equations”.
As usual, caution should be exercised in identifying the reality with the model, see also
a general discussion of potential limitations of models in
Section 5.1
. With that in mind,
however, such a Lagrangian model was capable of simulating the nonlinear behaviour of
wave trains and going far beyond the point where wave-breaking simulations by Eulerian
means would be stopped.
That is,
Tulin & Landrini
(
2001
) were able to model the breaking progress after break-
ing onset, including splashing, mixing and air entrainment, i.e. effectively to simulate a
multi-phase medium. The motion of individual particles is tracked, and thus the kinemat-
ics and dynamics of the primary and secondary plunging jets is investigated, formation of
the underwater vortical structures is analysed, and the collapse of the air cavity, series of
splash-up cycles and other breaking and post-breaking features are described. The authors
stressed that, technically speaking their method can also deal with weak compressibility
effects and thus potentially handle even acoustic-noise generation in the course of breaking.
This potential capacity of the method was achieved by a more recent SPH model of
Dalrymple & Rogers
(
2006
). The authors essentially extended earlier applications of the
SPH methods to free-surface fluid flows by improving and implementing the treatment of
water density, viscosity and turbulence.
By introducing the compressibility of the fluid, the
Dalrymple & Rogers
(
2006
) model
was able to produce sound associated with the breaking. This sound is one of the principal
proxies for wave-breaking events and associated passive-acoustic instrumentation is among
the most promising means of remote-sensing studies of wave breaking and dissipation (see
Section 3.5
). Examples shown in
Dalrymple & Rogers
(
2006
) for waves breaking at a
beach clearly and realistically exhibit the acoustic impact of breaking waves similar to
that in
Bass & Hey
(
1997
) and
Babanin
et al.
(
2001
)(seealso
Figures 3.1
and
3.4
in
this topic).
Modelling two-dimensional breaking at the beach realistically reproduced a number of
apparent and less apparent known features of shallow-water breaking, such as the plunging
jet, formation of vorticity, the splash-ups, including the reverse breaking occurrence and
associated downbursting all the way to interacting with the bottom. The latter two less
obvious features have independent observational support (
Li & Raichlen
,
2003
;
Kubo &
Sunamura
,
2001
).
Search WWH ::
Custom Search