A New Inverse Phase Speed Spectrum of Nonlinear Gravity Wind Waves

Abstract

The rear face of the wave spectrum is described by an equilibrium and a saturation subrange. Although accurate information about these ranges are highly relevant for wave modeling and many practical applications, there have been inconsistencies between results originating from temporal and spatial measurements. These discrepancies have been explained by the Doppler shift and the harmonics of nonlinear waves. We present high-frequency wave measurements from the Baltic Sea gathered with R/V Aranda using a wave staff array, which provided directional frequency-wavenumber data. In addition to the traditional wavenumber and frequency spectra, F(k) and S(ω), we also define a new spectrum that is a function of the inverse phase speed. We denote this spectrum Q(ν), where ν=kω−1. The properties of this Q-spectrum were studied using data from four different sites. A strongly forced fetch-limited case showed an equilibrium-to-saturation transition in the Q-spectrum, with less variations in the equilibrium constants compared to the frequency spectra. The transition to a saturation regime happened around Uν=3 in all spectra where an equilibrium range was identified. Most duration-limited spectra had no equilibrium range in the inverse phase speed domain. The absence of an equilibrium range was consistent with the wavenumber domain, but the frequency spectra still showed an apparent equilibrium subrange extending to ωU/g=5. The consistency of the saturation ranges between the Q-spectrum and the wavenumber spectrum indicate a weak Doppler shift effect. We deduced that the main factor distorting the frequency spectra was wave nonlinearities.