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 Of the three different velocity scales examined, the velocity referenced at a level
of 0.065 times the peak wavelength above the mean surface consistently provided the
scaling relationship with the lowest scatter around the regression line. In fact as shown in
Resio et al (2002), this scatter is reduced by a factor of three to four in high-quality,
small-basin data sets.
4. Discussion
As shown in Resio et al (2002), the findings here are consistent with a constant
flux of momentum from the atmosphere into the wave field, which agrees with the work
of Hasselmann et al (1973) and Resio and Perrie (1989). In fact, in the work by Resio
2
and Perrie (1989) was the initial basis for attemptin g the ua c p form as the scaling
parameter for β, after we had found that none of the forms based on wind speed along
gave a very good result.
2
The best-fit relationship for the entire data set was clearly achieved with the ur c p
scaling parameter. If we return the work of Resio and Perrie (1989), we see that they
included an analysis of laboratory data in their scaling analysis and showed that a
u120c p form provided a better fit to a wide range of data than did forms based on wind
speed alone; however, they did not have the extensive data shown here supporting that
conclusion in their paper. If we return to the data sets shown in their paper we see that
the use of ur improves the consistency of the β-ua relationship for lab data included.
These findings could potentially have significance to at least three several
practical applications. First, the interpretation of scatterometer data is roughly based on a
linear relationship between wind speed and measured return from wave fields. Since the
calibration of this relationship is based primarily on open-ocean data, it is possible that
the actual relationship is more of the form shown here. Second, wave models that depend
on detailed -balance arguments, typically have been calibrated to reflect either an ω -5
spectral form or a linear dependence of the energy levels in the equilibrium range on
wind speed. It is unlikely that either of these detailed -balance forms can work well over
a wide range of dynamic scales. And third, arguments of wave induced drag coefficients,
which are strongly dependent on wave age, are not supported by our findings.
Another point worth discussing in this paper is the fact that considerable evidence
accumulate. This is consistent with the expected behavior of spectral energy densities in
the equilibrium range, based on nonlinear energy fluxes; but it is difficult to see how any
wave breaking mechanism, which may be coerced to depend on f-4in deep water, can be
made to scale appropriately to reproduce this result. This appears to support arguments
that the primary energy losses within a wave spectrum are located in at high frequencies
and not in Regions I-III of the spectrum. It is also consistent with physical arguments
based on the depth of the "turbulence" (white-capping) region at the water surface during
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