Fully nonlinear analytical theories for surface waves and numerical simulations of wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 141

Dalrymple & Rogers ( 2006 ) went further and simulated three-dimensional breaking at
the beach. This revealed new spatial features such as the occurrence of counter-rotating
vortices which remained after the breaking wave had passed and continued descending
obliquely. Again, this feature finds independent experimental support ( Nadaoka et al. ,
1989 ). Demonstration of this capacity of the method is particularly important as breaking
is an essentially three-dimensional phenomenon (see e.g. Phillips et al. , 2001 ).
Therefore, the fully nonlinear models described in Sections 4.1 and 4.2 are sufficiently
self-consistent to approach the evolution of the steep wave train from initial conditions
which have no indication of any singularity in the system, all the way to incipient break-
ing. They also provide quantitative characteristics both for the wave train, in which the
breaking will occur, and for the individual wave, which will break. Lagrangian models
are potentially promising in further simulating the breaking-in-progress and post-breaking
effects in water, but are less developed and common at this stage. Further discussion on
models capable of reproducing the breaking in progress will be given in Section 7.2 dedi-
cated to simulations of wave-energy dissipation in two-phase models ( 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 ; Tulin &
Landrini , 2001 ; Hieu et al. , 2004 ; Song & Sirviente , 2004 ; Zhao et al. , 2004 ; Iafrati &
Campana , 2005 ; Dalrymple & Rogers , 2006 ; Lubin et al. , 2006 ; Liovic & Lakehal , 2007 ;
Iafrati , 2009 ; Dao et al. , 2010 ; Janssen & Krafczyk , 2010 ; Lakehal & Liovic , 2011 , among
others).
Thus, fully nonlinear numerical modelling allows us to move frommathematical abstrac-
tions to physical reasoning and verify the theoretical conclusions by experimental means.
Such verification will be discussed in Chapter 5 .