Role of wave breaking in the air–sea interaction - Breaking and Dissipation of Ocean Surface Waves - page 390

the wave breaking. Jacobs ( 1978 ), Pleskachevsky et al. ( 2001 , 2005 , 2011 ), Qiao et al.
( 2004 , 2008 , 2010 ) and Gayer et al. ( 2006 ) all came up with empirical or semi-empirical
arguments in favour of the wave-induced turbulence and suggested similar parameterisation
of an additional coefficient of turbulence diffusion, scaled by the wave amplitude.
In addition to the wave-turbulence diffusion, Pleskachevsky et al. ( 2011 ) introduced a
direct term of wave-turbulence production for Reynolds averaged Navier-Stokes schemes.
Here, we will follow this most recent update to describe such approaches.
In a sequence of studies dedicated to simulations of suspended bottom-sediment pro-
files in the North Sea (depths of 30-70m), Pleskachevsky et al. ( 2001 , 2005 , 2011 ) and
Gayer et al. ( 2006 ) found the connection between the intensity of turbulent diffusion in the
water column and the surface waves. Putting this simply, without introducing such diffu-
sion, it was not possible to describe the observed sediment profiles, and the wave-breaking
turbulence schemes such as that by Craig & Banner ( 1994 ) were not able to help in a
general case.
The turbulence intensity responded rapidly to the storms in the area, while models which
took account of the mean and drift currents for tides and wave breaking could not produce
such a response. Pleskachevsky et al. ( 2011 ), in particular, refer to satellite-borne ocean-
colour images of the North Sea, where plume-like patterns are visible, which are caused by
scattering the reflected sunlight at the suspended particulate matter. These patterns appear
in the sea areas following high-wave conditions and signal the bottom-sediment particles
being suspended during the storm and raised all the way from the bottom to the surface,
that is strong and rapid mixing.
Pleskachevsky et al. ( 2011 ) set on implementing the wave action directly into the equa-
tions for evolution of the turbulent kinetic energy, aiming to improve their circulation
model by taking into account the wave-induced diffusivity. The reference point was that
the real non-breaking wave-induced motion differs from the idealised mean-motion orbits
obtained from linear or nonlinear potential wave theories. The existence of random fluctua-
tions with respect to such mean motion has been confirmed experimentally in laboratories
( Babanin , 2006 ; Babanin & Haus , 2009 ; Dai et al. , 2010 ). These turbulent fluctuations
produce a small dissipation of the wave energy, spent on turbulence generation (see Sec-
tion 7.5 ), but most importantly they facilitate turbulent mixing through the water column
where such a source of turbulence is significant enough. Since the wave energy (and orbital
velocities) reach very high values during a storm, a slightest loss (unrelated to the break-
ing in this context), though relatively small for the waves, but being vertically distributed,
has a strong effect on the mean-flow properties through the respective turbulent mixing.
Therefore, Pleskachevsky et al. ( 2011 ) obtained a parameterisation based on the idealised
analytical solution of the wave motion (which describes the mean wave-velocity field well
enough as was argued by Babanin ( 2006 )) and implemented it into a k − turbulence model

(GOTM, Burchard et al. , 1999 ).
For clarity of the argument, Pleskachevsky et al. ( 2011 ) introduce what they call 'sym-
metrical' and 'asymmetrical' wave motion. The so-called symmetrical oscillations of the
individual waves relate to applications where the wave dissipation is not relevant or is not