Detection and measurement of wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 67

Significantly lower were the losses of kinetic energy Q (2.26) :

Q
Q before =

s kinetic = 20-25% . (3.25)

Such a difference is qualitatively consistent with recent observations. Young & Babanin
( 2006a ), when comparing spectra of pre-breaking and post-breaking waves, found some
40% of energy lost in the peak region of the surface-elevation power spectrum in the case
of dominant breaking, while the peak region of the velocity spectrum measured below the
wave troughs remained virtually unaltered.
An interesting account of a contact laboratory experiment with wind-generated waves
was provided by Leikin et al. ( 1995 ). It was dedicated to measurements of wave asymmetry
A s (1.3) , and although breaking detection was not conducted, discussion of these results is
relevant here.
Leikin et al. ( 1995 ) found a strong correlation of the asymmetry A s with inverse wave
age u

∗ /

c p , whereas correlations of skewness S k (1.2) and steepness (1.1) with wind

forcing were poor. Thus, they supposed that

“the vertical asymmetry of waves is caused by direct wind forcing”.

At the same time, they conducted bispectral analysis which revealed strong nonlinear
coupling between the main wave and its harmonics. Therefore, Leikin et al. ( 1995 )also
concluded that the observed wave system can be treated as mainly the dominant compo-
nent with its harmonics propagating at the same speed. Normally, such a system would
have non-zero skewness S k , but not, on average, non-zero asymmetry A s . Therefore, the
phase shift between the main component and the harmonics was considered and found to
increase with u c p , and thus explained the growth of vertical asymmetry.

The two conclusions, i.e. the direct influence of the wind on wave shape and this shape
being a result of bound nonlinear harmonics, seem contradictory. The first process sig-
nifies a strong air-sea interaction, whereas the second appears a purely hydrodynamic
phenomenon. The influence of the wind could perhaps be considered to be responsible for
the overall growth of the steepness and consequently the nonlinearity, including bound har-
monics, but such straightforward reasoning cannot explain the growing phase shift between
the carrier wave and the harmonics, and most importantly, there was in fact no correlated
growth of wave steepness as a function of wind forcing.
We would suggest a different explanation of the trend observed by Leikin et al. ( 1995 ).
At high wind forcing there is indeed a strong connection between the wind input into waves
and the asymmetry ( Agnon et al. , 2005 ). This connection, however, does not bring about
negative average asymmetry, it only causes correlated oscillations of the input and A s .In
our view, what makes the asymmetry non-zero on average (in the formulation of Leikin
et al. ( 1995 ) it is positive rather than negative for waves leaning forward) is wave breaking.
The range of wind speeds involved in the experiment was u ∗ =

∗ /

s which,
if converted into corresponding winds at a standard 10m height using (3.19) ,gives U 10 ≈
8-48m

0 . 27-1 . 71m /

/ s. These signify some very high wind speeds. Agnon et al. ( 2005 ) found that for