SURFACE GRAVITY AT EQUILIBRIUM WITH A STEADY WIND

Observations of wave fields' spatial evolution and of gravity, wave sp ectra S(omega) are analyzed on the basis of the data reported by sever al research groups as well as on a 2-year data set of wind and wave me asurements by stationary National Oceanic and Atmospheric Administrati on buoys near the Hawaiian Islands. We seek to clarify the role of the wave energy advection (with the wave group velocity) in the overall e nergy balance. This advective transfer appears to be no less important than the local (breaking wave induced) dissipation as a factor of win d-wave equilibrium. The advection is found to manifest. itself in the shape of wave spectra by reducing the rate at which the spectral densi ty of the wave energy, S(omega) approximately omega(-p), falls off as the frequency increases away from the spectral peak. This and other co nclusions are derived by comparing the field observations with theoret ical predictions of the weak turbulence theory for a spatially inhomog eneous, statistically stationary, wave field. The observations also in dicate that the typical wave age xi = C0/U in the open ocean is much g reater than the limiting value 1.2 attributed to the ''fully developed sea.'' Although the observed spectra can be approximated by a power l aw with a single ''effective'' exponent, this apparent exponent, p, is found to depend on the wave age. At high xi and at frequencies below the generation range, - p tends to - 3 rather than the value of - 11/3 predicted by the Zakharov-Zaslavskii theory. This deviation is interp reted as pointing to a nonconservative nature of the inverse cascade, the latter including a leakage of energy to low-wavenumber modes. Depe ndence of the overall effective exponent on xi is shown to be responsi ble for variation in the coefficients b, B, c, C appearing in empirica l fetch laws, such as xi = Cx(c) and e = Bx(b), where x and e are the dimensionless fetch and wave energy, respectively.