Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 209

Figure 5.36 Velocity spectrum V ( f ) measured at 10 cm , 20 cm , 30 cm , 40 cm , 50 cm and 60 cm dis-
tances from the surface for a 9 . 7m / s mean wind speed (the more energetic spectra are closer to the
surface). The Kolmogorov interval slope of f − 5 / 3 is shown with a straight line. Figure is reproduced
from Young & Babanin ( 2006a ) © American Meteorological Society. Reprinted with permission

10 cm increments and the six 20min-averaged spectra shown in Figure 5.36 were recorded
at 10 cm

50 cm and 60 cm from the mean water level, respectively.
The wind was steady in speed and direction over the two-hour time period of measuring
the profile, U 10

, 20 cm , 30 cm , 40 cm ,

= 9 . 7m / s on average, with a maximum of 10 . 9m / s and a minimum of

8 s. The more energetic spectra shown in Figure 5.36 were recorded closer to the

surface, with the energy level decaying with depth.
Dissipation rates

. 3m /

dis obtained on the basis of such spectra using (5.66) are shown in
Figure 5.37 . This figure plots

dis as a function of z in dimensionless form

function gz
u 2
∗ w

dis κ z

= (5.71)

u 3
∗ w

where u 4 is the von Karman constant, and the

mean water level is now treated as the wall. Wall-law scaling is applied to the dissipation
dis and height-of-fully-developed-waves scaling is applied to the distance to the surface
z (see Agrawal et al. , 1992 ; Melville , 1994 ). For boundary layers over solid walls, such
scaling of the dissipation would give values of

is the friction velocity in the water, κ ≈ 0 .

∗ w