Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 278

argued that most of the swell dissipation comes from the negative momentum/energy flux
from the swell field to the wind, and they formally included this kind of wave-energy
dissipation as an additional negative wind-input term (see also Harris , 1966 ; Vo l k o v , 1970 ;
Makin & Chalikov , 1980 ; Donelan , 1999 ; Drennan et al. , 1999 ; Grachev & Fairall , 2001 ;
Grachev et al. , 2003 ; Lavrenov , 2004 ; Babanin & Makin , 2008 ; Hanley et al. , 2010 ;
Soloviev & Kudryavtsev , 2010 , among others).
Here, we should note that swell dissipation, at least at initial stages of swell propagation
while it is still steep, can also be explained through generation of the wave turbulence,
unrelated to breaking (see Babanin , 2006 ; Babanin & Haus , 2009 ; Dai et al. , 2010 ,see
also Section 7.5 ). The relative strength of the swell friction against the air at the air-sea
interface and the swell's role in producing the wave-induced turbulence are unclear at this
stage. In Ardhuin et al. ( 2010 ), the swell dissipation was calibrated on the basis of satel-
lite observations of swell attenuation when propagating large distances across the ocean
( Ardhuin et al. , 2009a ).
Thus, Ardhuin et al. ( 2010 ) took dissipation-function modelling to very new heights.
While the formulations for the different sub-terms of the dissipation function are still
largely empirical and the tuning was still needed, the authors made an extraordinary effort
to accommodate most of the known up-to-date experimental features of the spectral dis-
sipation, and, where possible, used theoretical justification and experimentally observed
dependences for calibrations.
A variety of tests and validations were conducted. These covered both the standard set
of steady-wind fetch-limited growth according to Komen et al. ( 1984 ) and hindcasts of
real-life storms, on regional as well as global scales. The regional scales included such
diverse situations and water bodies as young waves in Lake Michigan and Hurricane Ivan
in the Gulf of Mexico. The hindcasts were conducted by means of WAVEWATCH-III TM
( Tolman , 2009 ) and demonstrated a potential for improvements in performance.
Such improvements do not necessarily come hand-in-hand with updating the physics
of models, which had been well-tuned to predicting standard situations over years. Incor-
poration of new dissipation features is more complex than a mere replacing of one dis-
sipation term with another. For example, if a cumulative integral is simply added to the
breaking-dissipation term, then local-in-wavenumber-space balance can no longer be sat-
isfied at smaller scales where the cumulation is significant, and re-formulations and adjust-
ments of the wind input function and potentially of the entire model will also be required.
Therefore, an essentially modified version of the Janssen ( 1991 ) input was employed by
Ardhuin et al. ( 2010 ) which, in turn, led to a markedly different spectral balance of the
source terms.
Another new implementation of the observation-based physics into source functions of
spectral wave models is that by Babanin et al. ( 2007d ), Tsagareli ( 2009 ), Tsagareli et al.
( 2010 ) and Babanin et al. ( 2010c ). In this case, both wind-input S in and dissipation S ds
terms in (2.61) are new and observations based. Mathematical expressions for these func-
tions are not based on any of the above-mentioned parameterisations presently employed
in wave models, and they were initially designed to accommodate new features observed