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 From these arguments it can be seen that a 20% increase in spectral densities in the
equilibrium range would result in over a 70% increase in the energy flux rates due to
nonlinear interactions. Thus, the nonlinear interactions should force a very strong
tendency toward the ω -4 spectral form even if wind input is occurring in this region of the
spectrum.
Region 4, the dissipative range, is the portion of the spectrum in which energy,
fluxed toward high frequencies via nonlinear interactions, is lost due to either turbulence
(breaking) or viscous effects. The low-frequency limit to this range should be
coincident with the point where the equilibrium range slope shifts to a steeper slope (ω -n
where n>4). This may occur over a range of frequencies and different researchers have
postulated different points at which this is expected to occur. For the purpose of this
paper, we will just assume that a high-frequency energy sink exists, one that is capable of
removing all energy fluxed into this region of the spectrum. Since this spectral region is
located at relatively high frequency, the exact shape of the spectrum in this region does
not affect most practical applications.
3. Data
Data selected for analysis here include one deep ocean buoy maintained by the
National Data Buoy Center (NDBC, http://www.ndbc.noaa.gov), one shallow ocean
sensor maintained by the U.S. Army Engineer Research and Development Center's Field
Research Facility (FRF, http://www.frf.usace.army.mil), and one site on the east side of
Lake George, Australia. Anemometers were located directly above wave sensors at all
sites except for FRF #630, where winds were measured at the landward end of the FRF
pier.
Four dimensionless parameters can be considered relative to site selection:
wave steepness H mok p , and inverse wave age ua / cp (often characterized as u10 / cp ).
The first of these has an approximate theoretical lower limit keqh ≈ 0.7 below which the
wavenumber dependence of the equilibrium range may change form, due to depth-related
changes in the behavior of coupling coefficient (Resio 1987). Zakharov (1999) has
shown that for keq h < 0.3 , the spectrum should asymptotically tend toward a k -4/3 form.
The subscript "eq" has been added to his original "kh" parameter to reflect the fact that
his theoretical argument is valid only within the equilibrium range and not in the spectral
peak region. With parameters defined in Sections 3.2 and 3.3, data from the above sites
have relative depths in the range 0.7 < keqh , which pushes the lower limit somewhat.
The data extends into very deep water at most deep -ocean sites.
4. Analysis
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