Analysis and Interpretation of Frequency–Wavenumber Spectra of Young Wind Waves

Abstract

The energy level and its directional distribution are key observations for understanding the energy balance in the wind-wave spectrum between wind-wave generation, nonlinear interactions, and dissipation. Here, properties of gravity waves are investigated from a fixed platform in the Black Sea, equipped with a stereo video system that resolves waves with frequency f up to 1.4 Hz and wavelengths from 0.6 to 11 m. One representative record is analyzed, corresponding to young wind waves with a peak frequency f p 5 0.33 Hz and a wind speed of 13 m s 21 . These measurements allow for a separation of the linear waves from the bound second-order harmonics. These harmonics are negligible for frequencies f up to 3 times f p but account for most of the energy at higher frequencies. The full spectrum is well described by a combination of linear components and the second-order spectrum. In the range 2f p to 4f p , the full frequency spectrum decays like f 25, which means a steeper decay of the linear spectrum. The directional spectrum exhibits a very pronounced bimodal distribution, with two peaks on either side of the wind direction, separated by 1508 at 4f p . This large separation is associated with a significant amount of energy traveling in opposite directions and thus sources of underwater acoustic and seismic noise. The magnitude of these sources can be quantified by the overlap integral I(f ), which is found to increase sharply from less than 0.01 at f 5 2f p to 0.11 at f 5 4f p and possibly up to 0.2 at f 5 5f p , close to the 0.5p value proposed in previous studies.

Observation of Extreme Sea Waves in a Space–Time Ensemble

“…The WASS setup at Acqua Alta is similar to that used in previous applications Leckler et al 2015) and consisted of a pair of 5 megapixel digital cameras (with 2456 columns by 2048 rows array of 3.45-mm square active elements) and mounting 5-mm distortionless lenses, placed 2.5 m apart and 12.5 m above the mean sea level.…”

“…As a consequence, we can keep a relatively small window size (13 3 13 pixels), while still obtain a precise localization of the matches. This accounts for the matching bias for points around white-capped areas described by Leckler et al (2015) without introducing brightness equalizations or complicated pyramidal search approaches. A discussion of the errors associated with the WASS measurements is reported in the study of Benetazzo et al (2012), from which we recall the mean absolute quantization error of the adopted WASS setup, which is on the order of 2-3 cm along the three camera axes.…”

“…Instrumentation, like radars (Rosenthal and Lehner 2008;Lehner and Gunther 2004), laser scanners (Hwang et al 2000a;Romero and Melville 2010), and stereo cameras (Wanek and Wu 2006;Benetazzo 2006;Kosnik and Dulov 2011;Benetazzo et al 2012;Gallego et al 2011), are indeed providing new samples of sea surface elevations h, for which the spatial dimensions x and y are added to the wave time records h(t), producing spatial h(x, y) or even space-time ensembles h(x, y, t) of wave data. These newly explored sets of observations led to new insights on sea waves behavior, including the speed of large wave crests (Banner et al 2014), the frequency and wavenumber distributions of sea waves (Hwang et al 2000b;Leckler et al 2015;Romero and Melville 2010), the spatial statistics of waves (Romero and Melville 2011), and some properties of the spatiotemporal wave groups (Nieto Borge et al 2013;Nieto Borge 2004).…”

Note on the directional properties of meter-scale gravity waves

“…Previous time-resolved measurements of ocean waves have clearly established a prevalence of directional bimodality at frequencies above twice the peak frequency f p , using in situ array (Young et al, 1995;Long and Resio, 2007) and buoy data (Ewans, 1998;Wang and Hwang, 2001). These were confirmed by airborne remote sensing techniques used by Hwang et al (2000) and Romero and Melville (2010).…”

Comprehensive Ground-Space Monitoring of Anthropogenic Impact on Russian Black Sea Coastal Water Areas

“…-A method of direct assessment of sea wave spatial spectra using wave buoy arrays. This method is based on the wavelet transform allowing for studying nonstationary phenomena [6,23]. -A method of sea surface multi-polarized radar imagery processing, when normalized radar cross-section (NRCS) is given as a sum of Bragg scattering-related polarized scattering and non-polarized scattering related with wave breaking [20].…”