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 mechanisms. In an attempt to avoid this problem, we postulate a theoretical framework
for wind-wave spectra during active wave generation as shown in Figure 4. In this
Figure, four spectral regions are defined, based roughly on the hypothesized controlling
forcing mechanisms for each region.
Region 1, the spectral peak region, is bounded at its upper limit by frequency f0,
which is a frequency at which there is no net nonlinear flux of energy and extends to zero
at its lower limit. Since there is no net flux of energy into or out of Region 1 due to
wave-wave interactions, the net gain or loss of energy in this region depends only on
external sources (wind input and wave breaking). The role of wave-wave interactions
region will likely relate to down-shifting of the spectral peak, due to the strong
asymmetry of this source term within this region.
Region 2, the transition region from Region 1 to the equilibrium range, is
range) at its upper boundary. This region represents an area in which nonlinear energy
fluxes become less and less influenced by the proximity to the spectral peak ( and low-
frequency cut-ff) as feq is approached. Since there is zero net energy flux across f0, we
will hypothesize here that the primary mechanisms controlling the shape of this region
are net wind input and wave-wave interactions. Under the assumption that wave
breaking is very small in this region, a positive flux of energy (i.e. a flux directed toward
high frequency) must exist at feq, in order to compensate for the energy gain in this
region.
Region 3, the equilibrium range, has been the subject of many studies (Zakharov
and Filen enko, 1966; Kitaigorodskii, 1983; Resio, 1987; Resio et al, 2001). It is assumed
dissipation begins to play a major role in the spectral energy balance. In the initial
derivation by Zakharov and Filenenko (1966), it was assumed that an ω -4 (where ω is
radial frequency) slope would exist in this region ( i.e. E(ω )∼ω -4, where E(ω ) is energy
density) in the absence of any external sources and sinks. However, since we know that
wind input exists at the spectral peak and at higher frequencies, it is extremely unlikely
that wind input is identically zero across the entire equilibrium range. Consequently, it
would appear that the requirement of no input should be relaxed to a sufficiently small
most deep -water data sets. Recently, Resio et al (2001) showed that a more general form
for the equilibrium range could be written in term of a wav enumber spectrum,
α4
us g -1 / 2k -5 / 2
F (k ) =
(1)
2
where F(k) is the energy density in wavenumber space, α4 is a universal constant, us is a
scaling velocity , g is gravity, and k is wavenumber.
We assume that all three traditional deep -water source terms, wind input (S in),
nonlinear wave-wave interactions (S nl), and wave breaking (S ds), occur in all regions of
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