Time–frequency analysis of the sea state with the Andrea freak wave

Abstract

Abstract. The nonlinear and nonstationary properties of a special field wave record are analysed with the Wigner spectrum with the Choi-Williams kernel. The wave time series, which was recorded at the Ekofisk complex in the central North Sea at 00:40 UTC (universal time coordinated) on 9 November 2007, contains an abnormally high wave known as the "Andrea" wave. The ability of the Wigner spectrum to reveal the wave energy distribution in frequency and time is demonstrated. The results are compared with previous investigations for different sea states and also the state with Draupner's abnormal "New Year" wave.

Localized coherence of freak waves

“…Afterwards, the long waves will be in front of the short waves and the amplitude of the wave train will decrease (Kharif and Pelinovsky, 2003). This mechanism is observed in the type of dispersive focusing waves which are often used in hydrodynamic laboratories (Merkoune et al, 2013;Brown and Jensen, 2001;Clauss, 2002;Shemer et al, 2007Shemer et al, , 2005Grue et al, 2003). In random waves, this mechanism could also trigger a freak wave, but it is not as clear as in the dispersive focusing case.…”

“…In this paper, we investigate the local coherence computed from the local time spreading of the most energetic waves, which is determined by wavelet transform. Nowadays, wavelet transformation is widely applied to analyze freak waves (Hu et al, 2015;Kwon et al, 2015;Cherneva and Guedes Soares, 2014;Bai et al, 2015;Wang et al, 2015;Wu et al, 2010), as it has wider applicability than Fourier techniques (Lin and Liu, 2004).…”

“…In unidirectional linear waves, the focusing due to dispersion is one mechanism that causes a freak wave (Porubov et al, 2005;Slunyaev et al, 2005;Kharif et al, 2001;Brown and Jensen, 2001;Pelinovsky et al, 2000;Baldock et al, 1996). If short waves with small group velocities are initially located in front of long waves having large group velocities, the long waves will overtake the short waves with increasing time and large-amplitude waves can appear.…”

Comment to referee 2

“…In this paper, we investigate the local coherence computed from the local time spreading of the most energetic waves, which is determined by wavelet transform. Nowadays, wavelet transformation is widely applied to analyze freak waves (Hu et al, 2015;Kwon et al, 2015;Cherneva and Guedes Soares, 2014;Bai et al, 2015;Wang et al, 2015;Wu et al, 2010), as it has wider applicability than Fourier techniques (Lin and Liu, 2004).…”

Freak wave

“…In this paper, we investigate the local coherence computed from the local time spreading of the most energetic waves, which is determined by wavelet transform. Nowadays, wavelet transformation is widely applied to analyze freak waves [Hu et al, 2015, Kwon et al, 2015, Cherneva and Soares, 2014, Bai et al, 2015, Wang et al, 2015, Wu et al, 2010 as it has wider applicability than Fourier techniques [Lin and Liu, 2004].…”