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is still the case, but with the modern rate of development of computing facilities essen-
tial two-phase modelling efforts become increasingly feasible. Besides, the breaking in
progress as such is only short, a few periods at most including all the turbulent, spray and
bubble consequences. Long is the evolution from background conditions to the breaking
onset, and that part is simulated very well by fully nonlinear potential models whose com-
putational cost is much less (e.g. Dommermuth et al. , 1988 ; Chalikov & Sheinin , 1998 ,
2005 ). Thus, the whole breaking-dissipation process can be covered if the potential-model
outputs are connected with the two-phase model input.
Lagrangian models of this type ( Tulin & Landrini , 2001 ; Dalrymple & Rogers , 2006 ;
Dao et al. , 2010 ) have been mentioned and described in some detail in Section 4.2 .
Lagrangian models are very efficient in handling the nonlinearities of flow processes
involved, but have to deal with the conservation issues for fundamental physical prop-
erties. Those issues appear to be solvable and therefore it should be a matter of time and
dedicated effort to test and use this model for wave-energy dissipation studies.
A number of elaborate non-Lagrangian methodologies were also developed in compu-
tational fluid dynamics, and then applied to modelling breaking in progress ( Abadie et al. ,
1998 ; Zhao & Tanimoto , 1998 ; Chen et al. , 1999 ; Watanabe & Saeki , 1999 ; Mutsuda &
Yasuda , 2000 ; Christensen & Deigaard , 2001 ; Grilli et al. , 2001 ; Guignard et al. , 2001 ;
Hieu et al. , 2004 ; Song & Sirviente , 2004 ; Zhao et al. , 2004 ; Iafrati & Campana , 2005 ;
Lubin et al. , 2006 ; Liovic & Lakehal , 2007 ; Iafrati , 2009 ; Janssen & Krafczyk , 2010 ;
Lakehal & Liovic , 2011 , among others). Some allow us to combine an Eulerian model with
Lagrangian free-surface tracking (e.g. Grilli et al. , 2001 ; Guignard et al. , 2001 ; Janssen
& Krafczyk , 2010 ). Others use direct numerical simulations combined with sophisticated
techniques for capturing the interface (e.g. Abadie et al. , 1998 ; Zhao & Tanimoto , 1998 ;
Chen et al. , 1999 ; Song & Sirviente , 2004 ; Iafrati & Campana , 2005 ; Lubin et al. , 2006 ;
Liovic & Lakehal , 2007 ; Iafrati , 2009 ; Lakehal & Liovic , 2011 ). Some assume the grid
size to be refined enough to take into account scales as small as necessary (e.g. Abadie
et al. , 1998 ; Chen et al. , 1999 ; Grilli et al. , 2001 ; Guignard et al. , 2001 ; Song & Sirviente ,
2004 ; Iafrati & Campana , 2005 ; Iafrati , 2009 ; Janssen & Krafczyk , 2010 ). Others combine
direct numerical simulations with special treatment of the small-scale processes by means
of the large eddy simulation (LES) method (e.g. Zhao & Tanimoto , 1998 ; Christensen &
Deigaard , 2001 ; Lubin et al. , 2006 ; Liovic & Lakehal , 2007 ; Lakehal & Liovic , 2011 )or
the Reynolds average Navier Stokes approaches (e.g. Zhao et al. , 2004 ). All of these meth-
ods have an apparent potential capacity to address the wave-dissipation problem explicitly,
and in this regard intercomparison of the outcomes some time down the track would be
most instructive.
Here, we will briefly review the study by Iafrati ( 2009 ) who, among other physical prob-
lems, specifically investigated dissipation rates in the course of breaking progress, i.e. the
topic of the present section. This was done for a single two-dimensional wave of steepness
=
ak
cos
a
λ
1
2 ·
3
8
2 cos
η(
x
) =
(
kx
) +
cos
(
2 kx
) +
(
3 kx
)
(7.8)
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