Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 275

a methodology of separate independent calibration of the wind-input S in and dissipation
S ds functions.
At present, when modelling equation (2.61) , there is almost no flexibility in formulating
S nl and some limited flexibility in formulating S in . By contrast, functions to represent
S ds still can be chosen rather arbitrarily and are used in models without much objection
from the wave-modelling community. There is no consistency and sometimes even little
similarity between the terms of Komen et al. ( 1984 ), Polnikov ( 1991 ), Tolman & Chalikov
( 1996 ), Babanin et al. ( 2007d , 2010c ), Van der Westhuysen et al. ( 2007 ) and Ardhuin et al.
( 2010 ), all of which are incorporated in models and used alongside some standard terms
for S nl and S in .
The latter two are based on more or less defined physics (e.g. Hasselmann ( 1962 ) and
Donelan et al. ( 2006 ), respectively). Obviously, all the formulations for the dissipation
S ds refer to some physics too, but theoretical and experimental guidance had been very
uncertain in the past.
Existing theories of the wave-breaking dissipation, both their advantages and shortcom-
ings, were analysed in Section 7.1 . In short, it is generally assumed that the spectral
dissipation S ds ( . Since the

functional form of this dependence is basically unknown, the dissipation is usually param-
eterised as an algebraic power function of omni-directional spectrum F

f , k ,θ) in (2.61) depends on the wave spectrum ( f , k ,θ)

( f ) (see eq. 7.1 ).

Some directional distribution is then assumed, typically isotropic.
It would be fair to mention that, in spite of a relatively broad choice of theoretical
models in Section 7.1 , it is the theory by Hasselmann ( 1974 ) which is most frequently
referred to in S ds formulations. From the very beginning, however (i.e. Komen et al. ,
1984 ), this theory was employed only conditionally - that is, speculative properties and
parameters were added to meet tuning needs, and in particular to compensate for the
missing threshold behaviour and cumulative effect as was discussed, in particular, in
Section 7.3.4 above. Over the years, this term has undergone a significant number of simi-
larly speculative alterations and additions, a review of which is available in Appendix A of
Ardhuin et al. ( 2007 ).
Contrary to the theory of dissipation, recent experimental advances in wave-dissipation
studies have brought about much more certainty regarding the behaviour of S ds . In our
view, the notion that the dissipation function is a great unknown and that any formulation
that helps to satisfy the energy balance is considered legitimate, is no longer satisfactory.
Over the past decade, many physical features of the dissipation performance have been dis-
covered experimentally and explained as described throughout this topic and this chapter.
How are these physics, which are by no means tentative reasoning, but are definite field
observations, included in S ds terms? In WAVEWATCH (see Tolman , 2009 , for the latest
version of this model), two-phase behaviour of the dissipations term is accommodated, i.e.
that it is different at the spectral peak and the spectrum tail (although the assumed physics
of Tolman & Chalikov ( 1996 ) is different to that revealed in the experiments by Babanin &
Young ( 2005 ), Young &Babanin ( 2006a ) and Manasseh et al. ( 2006 )). Rogers et al. ( 2003 ),
in a way, attempted to introduce a threshold-dissipation behaviour by disallowing the