Role of wave breaking in the air–sea interaction - Breaking and Dissipation of Ocean Surface Waves - page 393

that is M current is the shear frequency due to the respective mean-current component U i .
The eddy viscosity due to the mean-flow currents is usually defined as

√ Kl

ν t = ν current = c , (9.36)

μ

with stability function c μ and length scale l .
Now, to take the wave motion into account in the circulation model, Pleskachevsky et al.
( 2011 ) decomposes the overall wave motion into two parts and parameterises them separ-
ately. The sub-processes occur on a dt T micro-time scale and the mean-flow processes

occur on the coarser dT mean mean-flow scale. Following the definitions above, the sub-
processes will be referred to as symmetric motion, and mean-flow processes as asymmetric
motion.
Symmetric motion (SM), if integrated, does not contribute to the mean currents (the
mean horizontal velocity, for example, due to such motion is zero; hence the motion is sym-
metric), but during time dT mean ,onthe dt -scale, a strong influence of waves on turbulence
is possible. The impact of SM on the flow can be parameterised using shear

<

M S wave = M wave , (9.37)

from (9.33) . Note that M wave uses wave parameters H , T and k . These integral parameters
are obtained from the wave spectra, estimated by the wave model with the dissipation
accounted for. Various implementations of this effect have been conducted before (e.g.
Jacobs , 1978 ; Pleskachevsky et al. , 2001 , 2005 ; Qiao et al. , 2004 , 2010 ; Gayer et al. ,
2006 ).
Asymmetric motion (AM) represents the dissipation of the primary wave motion: the
orbital tracks are no longer closed due to the damping, and the mean flow gains a weak
residu al-current effect. The asymmetric component can be parameterised by using shear
M wave and by employing ratio k AM

wave between wave energy dissipated and total wave energy:
M AM k AM

wave = wave M wave .

(9.38)

Coefficient k AM

wave here signifies the degree of efficiency of wave-energy dissipation:

E diss
E

k AM
wave

= (9.39)

where E diss means the depth-integrated dissipated wave energy per unit of surface, and E
is the wave energy in (2.23) before the dissipation is taken into account by the wave model.
Now, we can summarise the wave effect, both SM and AM parts, in (9.34) . First, the
TKE production has to be increased by the additional wave source:

P wave = ν t M AM 2

.

(9.40)

wave

This is the asymmetric part of the wave motion which influences the mean flow U directly:

P wave = ν t M current +

wave .

M AM 2

P S = P current + (9.41)