Surface gravity waves at equilibrium with a steady wind

Abstract

Observations of wave fields' spatial evolution and of gravity wave spectra S(ω) are analyzed on the basis of the data reported by several research groups as well as on a 2‐year data set of wind and wave measurements by stationary National Oceanic and Atmospheric Administration buoys near the Hawaiian Islands. We seek to clarify the role of the wave energy advection (with the wave group velocity) in the overall energy balance. This advective transfer appears to be no less important than the local (breaking wave induced) dissipation as a factor of wind‐wave equilibrium. The advection is found to manifest itself in the shape of wave spectra by reducing the rate at which the spectral density of the wave energy, S(ω) ∼ ω−p, falls off as the frequency increases away from the spectral peak. This and other conclusions are derived by comparing the field observations with theoretical predictions of the weak turbulence theory for a spatially inhomogeneous, statistically stationary, wave field. The observations also indicate that the typical wave age ξ = C0/U in the open ocean is much greater than the limiting value 1.2 attributed to the “fully developed sea.” Although the observed spectra can be approximated by a power law with a single “effective” exponent, this apparent exponent, p, is found to depend on the wave age. At high ξ 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 interpreted as pointing to a nonconservative nature of the inverse cascade, the latter including a leakage of energy to low‐wavenumber modes. Dependence of the overall effective exponent on ξ is shown to be responsible for variation in the coefficients b, B, c, C appearing in empirical fetch laws, such as and , where and e are the dimensionless fetch and wave energy, respectively.