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9_Resio_ Long

Figure 5 shows a plot of the band-averaged valued for ξ as a function of f/fp, for

all three data sets described later in this paper. In this Figure, the subscript "p" denotes a

value at the spectral peak. Also shown in this Figure are the curves for k-3 (ω -5 equivalent

in deep water) and k-2 (ω -3 equivalent in deep water) spectra, which clearly do not fit the

data very well. Even though some random deviations and some possibly periodic

variations in the value of ξ are seen, the general tendency is for ξ to remain

approximately constant in all of the data sets.

Since we are interested here in an integral balance of energy, rather than a

detailed frequency-direction balance, we shall not attempt to build upon different source

term forms; rather, we shall examine six types of wind-input scaling. These can be

written in the form:

feq

∫

Sin ( f ) df ~ ua

(7)

and

feq

∫

Sin ( f )df ~ ua cp

(8)

where cp is the phase speed of waves at the spectral peak, ua is a scaling parameter with

units of velocity, taken here to be 1) the wind speed at a reference level of 10 meters (u10)

; 2) the friction velocity (u* =τ1/2/ρa, where τ is the wind stress and ρa is air density); and

3) the wind speed at a fractional height of the wavelength of the spectral peak (u λ as

defined in Resio, et al., 1999). Thus, the six scaling combinations investigated here

consist of three different scaling parameters for wind speed inserted into the two different

scaling forms shown in equations 7 and 8.

4. Results

Figures 6a-6c show a plot of β versus

, where ua, in turn, represents the three

scaling options based on wind speed parameters only. Clearly, this scaling option does

not provide a unified scaling form for the different data sets. Instead, the slope of the

small-basin data (Lake George) is considerably shallower than the slope of the open

ocean data sets (FRF #630 and NDBC 46035). Figures 7a-7c show a plot of β versus

, where ua, in turn, represents the three scaling options based on wind speed and

phase velocity parameters in the manner described above. This scaling velocity provides

a basis for the data in the slopes of each data set are all consistent. Thus, this scaling,

rather than a scaling based on wind speed alone, provides a better, scale-independent

representation for energy densities in the equilibrium range.