Role of wave breaking in the air–sea interaction - Breaking and Dissipation of Ocean Surface Waves - page 394

In order to account for the influence of the symmetric component, the eddy viscosity has
to be modified by viscosity from the wave action

ν wave :

ν t = ν current + ν wave . (9.42)

These are sub-scale effects in the circulation models, and the standard closure hypothesis
is adopted (e.g. Kapitza , 2002 ):

l wave M S wave ν wave = (9.43)

where l wave is the length scale for the wave-induced turbulence. Following the argument of
Qiao et al. ( 2004 ) and Babanin ( 2006 ), l wave is assumed to be proportional to the wave
amplitude (radius of the wave orbit) which characterises the motion scale of physical
particles in the waves:

H
2

cosh ( k ( z + d ))

l wave ( z ) = α · a ( z ) = α . (9.44)

sinh ( kd )

The proportionality coefficient was set to 1in Qiao et al. ( 2004 ), and Dai et al. ( 2010 )

and Pleskachevsky et al. ( 2011 ), but there are indications that it can be smaller than that.
Finally, the TKE production term P S can be summarised by taking into account the wave
effects of both SM and AM components:
P S = (ν current + ν wave ) M current +

α =

wave .

M AM 2

(9.45)

This version of the production term describes the mean flow and includes the wave effects.
The symmetric part of the wave motion modifies the turbulent viscous term (influences the
mean velocity U through the eddy viscosity). The asymmetric part of the wave motion, due
to dissipation of the wave energy, imparts the mean current directly and appears explicitly
in the term for shear frequency.
To complete the wave-mixing scheme, the transition from laminar to turbulent wave
motion has to be parameterised too. This is achieved by using the critical Wave Reynolds
Number (7.67) suggested by Babanin ( 2006 ).
Pleskachevsky et al. ( 2011 ) continued on to successfully simulate the laboratory exper-
iment with an explosion-like transition from laminar to turbulent wave motion (i.e. the
experiment with dissolution of dye in Babanin , 2006 , see also Section 7.5 and Figure 7.21 )
and the North Sea observations of suspended particular matter. As mentioned above, simi-
lar schemes were used by Qiao et al. ( 2004 , 2010 ) on a global scale, where a wave model
was explicitly coupled with ocean-circulation models.
Results of Qiao et al. ( 2010 ) are particularly impressive. The influence of the wave-
diffusion term ν wave was tested using the Princeton Ocean Model (POM) and compared

with the standard Mellor-Yamada scheme which does not include the wave effects. With
the wave-induced (non-breaking) turbulent diffusion, the performance of the model in pre-
dicting sea surface temperature, the vertical thermal structure in the upper ocean and depth
of the mixed layer - all improved dramatically at latitudes where the wave activity is signif-