Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 297

the ocean is always turbulent (see e.g. Thorpe , 2005 ). A number of mechanisms of interac-
tion of waves with such a background turbulence have been proposed (e.g.
Kinsman , 1965 ; Kitaigorodski et al. , 1983 ; Cheung & Street , 1988 ; Jiang et al. , 1990 ;
Benilov et al. , 1993 ; Drennan et al. , 1997 ; Teixeira & Belcher , 2002 ; Ardhuin & Jenkins ,
2006 , among others). These result in passing the energy to the turbulence and mean cir-
culation which is therefore, as far as the wave fields are concerned, dissipation of wave
energy. The mechanisms include, for example, scattering the waves by water turbulence or
stretching the small-scale turbulence by the waves.
A separate large group of wave-turbulence interactions is generation of Langmuir cells.
These can be interpreted as a large-scale turbulence produced by the surface waves (e.g.
Langmuir , 1938 ; Craik & Leibovich , 1976 ; Smith , 1992 , 1998 ; McWilliams et al. , 1997 ;
Melville et al. , 1998 ; Phillips , 1998 , 2001 , 2002 , 2003 , 2005 ; Thorpe , 2004 ; Sullivan &
McWilliams , 2010 ).
Interactions of waves with water turbulence can certainly be energetic, to the point of
being an essential dissipation sink for, for example, short waves in the intensive surface-
turbulence wake of larger breakers (e.g. Banner et al. , 1989 , see also discussion in
Section 7.3.4 ). For longer waves, with periods in excess of 10 s, however, such mechanisms
appear not to be intensive enough to explain the observed wave-energy decay of swell. Ard-
huin & Jenkins ( 2006 ) compared swell-attenuation rates measured in ocean observations,
as well as those empirically inferred in operational wave models, with viscous and wind-
caused ( Kudryavtsev & Makin , 2004 ) damping and concluded that wave interaction with
oceanic turbulence is too weak to justify the observed decay.
Rather, Ardhuin et al. ( 2009a ) presumed that the decay is due to the swell interacting
with the turbulent boundary layer on the atmospheric side. They found that estimates of
such decay, based on analogy with the turbulent boundary layer, are not inconsistent with
the measurement.
Wind-wave interaction can be due to work done by normal (pressure) or tangential
(shear) stresses imparted by the waves on the air flow in the wave boundary layer, the
bottom sublayer of the atmospheric boundary layer (see e.g. recent publications by
Kudryavtsev et al. , 2001 and Chalikov & Rainchik , 2011 , among many others). It is gener-
ally accepted that, as far as the energy input from the wind to the waves is concerned, the
normal stresses drive the interaction (see e.g. Donelan et al. , 2006 and The WISE Group ,
2007 , for recent reviews of this topic).
For the swell, which gives the energy/momentum back to the air, Ardhuin et al. ( 2009a )
found no apparent connection between swell energy decay and the wind speed or swell age
c

U 10 . Therefore, they argued that the normal-stress interaction can be neglected, and they
considered only the shear-stress modulations imposed by the wave orbital motion. Here,
we should mention that the swell-induced wind is necessarily small in absolute magnitude,
even according to the most extreme estimates of its significance (see e.g. Donelan , 1999 ;
Lavrenov , 2004 ), and therefore such a correlation would be difficult to measure in the
field where background winds, unrelated to the swell, would almost always be expected to
prevail. This wind, however, is by far not insignificant ( Hanley et al. , 2010 ). Whatever the

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