Equations for the transfer of momentum and energy from air to water are applied to the “dominant” waves whose properties are defined statistically.
A growth rate consistent with that observed for “young” waves comes from assuming the dominant waves to have constant steepness during growth, and from assuming a constant form-drag coefficient
Cf0 for these waves. When referred to a level of 10 meters
Cf0 is only about 20 percent of the skin friction coefficient
Css, for a smooth surface (
Css≅. 0008). This constant value for
Cf0 begins to apply for fetches greater than about 15 m and wavelengths greater than about 10cm. It gives growth of dominant-wave height as
t2/3 and
x1/2 for the duration-and fetch-limited cases, respectively.
When appied to a sinusoidal wave of constant length and growing steepness, this aero-dynamic theory gives the respective growth-rate forms of Phillips' and Miles' theories upon making the appropriate assumption about
Cf0. The value of
Cf0 found for young waves (
Cf0=1.7×10
-4) implies the value β=1.4 for Miles' sheltering coefficient, s=. 011 for Jeffrey's sheltering coefficient, and
Cdw=1.3×10
-4 for Stewart's wave-drag coefficient applied to the dominant waves.
The approach toward equilibrium wave height is treated by referring the dominant-wave form drag to the wind-minus-wave speed at the r. m. s. crest level. The theory cannot explain dominant-wave speeds greater than the average wind speed at this level.
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