Non-dissipative effects of breaking on the wave field - Breaking and Dissipation of Ocean Surface Waves - page 335

A subsequent paper by Donelan et al. ( 2006 ) described prevailing environmental con-
ditions and presented new results on the physics and parameterisation of the spectral
wind-input source function for the wave field. One of the major outcomes reported in
this paper was the finding that the customary exponential growth rate parameter (fractional
energy increase per radian) depended on the mean steepness of the waves (i.e. the wind-
input term S in in RTE (2.61) is a nonlinear function of the wave spectrum, with growth
rates going up if the steepness was increasing).
Another major finding arose in the context of very strong forcing of steep non-breaking
waves, where a condition of 'full' separation was observed. It was argued that the full
separation occurs when the local surface curvature at the crest becomes too large for the
pressure gradient normal to the wave to be able to balance the centrifugal acceleration of
the wind layer in contact with the water surface. During the full separation of the wind flow
over a steep wave crest, the streamlines detach near the steep crest and do not reattach until
well up the windward face of the preceding wave towards its crest. The consequence is that
the shear layer, which is normally adjacent to the surface, detaches and moves upwards to
leave a 'dead zone' in the trough region between the crests. Thus, the external flow passes
over the wave troughs and the imposed pressure pattern is weaker than in the usual case
of non-separated flow. In a way, the wind 'does not know' how deep the wave troughs
are and responds to what 'it thinks' are much smaller amplitude waves. The phase shift
of the pressure maximum towards the re-attachment point on the windward face of the
wave, however, becomes larger. It was not immediately obvious whether the combined
effect would cause enhancement or reduction of the dimensionless wind input, but the
quantitative estimates exhibited a significant reduction, compared to the extrapolated input
at the same wave frequencies for the same wind forcing if the full-separation effects were
not taken into account.
It should be specifically stressed that the full separation of Donelan et al. ( 2006 ) and
the breaking-caused separation discussed in this section lead to different consequences.
In this regard, the flow separation due to wave breaking considered here does not corre-
spond to the full separation: it does somewhat increase the phase shift of the induced-
pressure maximum with respect to the wave trough, but the flow does not pass over the
wave troughs altogether as in the case of the full separation. As a result, there is an enhance-
ment rather than reduction of the wave-induced pressure magnitude, plus the increased
phase shift, and the flow separation due to breaking was always found to lead to enhance-
ment of the wind input in the field conditions, as described below. Qualitative comparison
of the two separation effects is sketched in Figure 8.2 .
Things can prove different in the laboratory, that is in conditions when the wind for-
cing is strong and the waves are steep and also very short. The separation due to breaking
can cause skipping of the wave troughs altogether, that is to bring about the full separ-
ation effect due to the breaking in such conditions. This is how Kudryavtsev & Makin
( 2007 ) explain the laboratory experiment of Donelan et al. ( 2004 ) with the surface-drag
saturation. And this is why laboratory measurements of wind input S in , as a function
of wave steepness, indicate negative rather than positive correlation with the high wave