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very significant deviations from the linear theory predictions, both overestimations and
underestimations of anticipated depth-dependent wave characteristics, have been reported
(see, for example, Cavaleri et al. , 1978 ,forareview).
At this stage, a few further words of caution with regard to the linear theory have to be
mentioned. As said above, ocean waves of lengths
1m, if described by the perturbation
theory based on the Euler equation, are considered free, with no viscosity and surface ten-
sion (e.g. Komen et al. , 1994 ). Such assumptions further lead to conjecture that the waves
happen to be irrotational. Although the former assumptions are a mere approximation and
justified in most cases (with noticeable faults in other cases, as mentioned above, though),
the latter feature of irrotationality imposes a serious limitation on the wave motion because
it basically bans wave-induced turbulence (although some theoretical mechanisms of gen-
erating the turbulence by irrotational waves are still possible, provided some background
turbulence exists, as discussed above in this section).
There is, however, accumulating evidence, both direct and indirect, that such turbulence
does exist. For example, as far as 40 years ago, Yefimov & Khristoforov ( 1971 ) concluded
that their measurements provide
λ>
“a basis for assuming that small-scale turbulence is generated by the motion of waves of fundamental
dimensions”.
They did not mention explicitly whether those waves were breaking or not, and Babanin
( 2006 ) conducted estimates based on the breaking-threshold criteria of Babanin et al.
( 2001 ). He concluded that, for the two records analysed by Yefimov & Khristoforov ( 1971 )
in their Fig. 5, breaking rates of dominant waves were 0.4% and 0.01%. Both rates are
marginal, the second one being negligible, and we have to conclude that the observed sub-
stantial levels of wave-associated turbulence could not have been brought about by wave
breaking, but were induced by the mean wave motion.
Cavaleri & Zecchetto ( 1987 ) in their dedicated and thorough measurements of wave-
induced Reynolds stresses gave explicit accounts for wave breaking. One set of their data
corresponds to active wind-forcing conditions (many breakers present are mentioned),
whereas the other set describes steep swell (no breaking). Non-zero vertical momentum
fluxes in the absence of breaking are evident. The magnitude of the fluxes appears to
depend quadratically on the height of individual waves which is consistent with the wave-
amplitude-based Reynolds number hypothesis (7.70) below. Cavaleri & Zecchetto ( 1987 )
concluded that
“in the water boundary layer there can occur an additional mechanism of generation of turbulence ...
full, correct description of the phenomenon is still lacking”.
Later, Babanin et al. ( 2005 ) conducted simultaneous measurements of the wind-energy
input rate and the wave-energy dissipation through a water column at Lake George (see
Sections 3.5 and 5.3.4 ). They showed that, at light winds and in the absence of wave break-
ing, turbulence persisted through the entire water column, not only in the shear boundary
layers near the surface and bottom. In the finite-depth lake, with no currents and internal
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