Role of wave breaking in the air–sea interaction - Breaking and Dissipation of Ocean Surface Waves - page 379

a)

WBL

T D , E V

T O , E

WW MLC

τ C , E C

E T E CT

MLT

b)

I Free atmosphere

entrainment
vertical velocities
Outer BL

h e

II

h s

III Monin-Obukhov BL

h w

IV WBL

ω ω r

ω > ω r

<

ζ r

V

0 s

VI

-ht

VII Mixed layer

entrainment
vertical velocities
Thermocline

-hm

VIII

Figure 9.8 a) Scheme of energy and momentum exchange between Wave Boundary Layer (WBL),
Wind Waves (WW), Mixed Layer Currents (MLC) and Mixed Layer Turbulence (MLT). Here, τ 0 is
the momentum exchange between WBL and WW (9.20) , τ c between WW and MLC (9.21) ,and T r
between WBL and MLC (9.19) . E is the energy exchange between WBL and WW (9.22) ,E c between
WW and MLC (9.23) ,E between WBL and MLC (9.24) ,E T between WW and MLT (9.25) ,and

E cT between MLC and MLT. b) General scheme for the atmosphere-ocean interactions. Figure is
reproduced from Chalikov & Belevich ( 1993 ) with kind permission from Springer Science+Business
Media

v

The momentum flux from wind to waves is
τ 0 = ρ w g ω r
0

π

(ω, θ)β(ω, θ) θ ω

k F d d (9.20)

− π

where is the wave fractional-growth coefficient (see e.g. Donelan et al. , 2006 ,

for detailed definitions of the wave-growth coefficients). The momentum transferred from
waves to currents because of wave breaking is equal to

β(ω,θ)