A New Inverse Phase Speed Spectrum of Nonlinear Gravity Wind Waves

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(omega), we also define a new spectrum that is a function of the inverse phase speed. We denote this spectrum Q(nu), where nu=k omega(-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 U nu=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 omega U/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. Plain Language Summary Surface waves are studied by partitioning them according to their length expressed in wave periods (seconds) or wavelengths (meters). Both approaches should give a similar descriptions of the waves, but in practice they produce inconsistent results. This limits our fundamental knowledge of waves and complicates practical applications. Measuring the wave period and the wavelength simultaneously is difficult, and there are not a lot of good data to study this problem. We measured the waves in the Baltic Sea from the ship R/V Aranda by recording the water level elevations using several thin submerged wires. From these observations we could describe the waves using both wave periods and wavelengths. The central part of our work was presenting the waves in a new way: We combined the wavelength and period measurements and partitioned the waves according to the speed which with they travel. The new partitioning shed light on the physical processes responsible for the discrepancies between the two traditional ways of representing the waves. This new approach might turn out to be useful, since many properties of the waves-such as the energy transfer from the wind-are controlled by their speed relative to the wind.