Observation of strongly non-Gaussian statistics for random sea surface gravity waves in wave flume experiments

Abstract

We study random surface gravity wave fields and address the formation of large-amplitude waves in a laboratory environment. Experiments are performed in one of the largest wave tank facilities in the world. We present experimental evidence that the tail of the probability density function for wave height strongly depends on the Benjamin-Feir index (BFI)-i.e., the ratio between wave steepness and spectral bandwidth. While for a small BFI the probability density functions obtained experimentally are consistent with the Rayleigh distribution, for a large BFI the Rayleigh distribution clearly underestimates the probability of large events. These results confirm experimentally the fact that large-amplitude waves in random spectra may result from the modulational instability.

Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation

“…Recent experiments in water waves [26], [9] and in fibre optics [31], [21], [22], [16] (see also review articles [5], [10]) have convincingly demonstrated that rogue waves are a generic physical phenomenon deserving a comprehensive investigation [27], [5]. It has also been understood that rogue waves play important role in the characterization of the nonlinear stage of modulational instability [41], [17] and particularly, in the development of integrable turbulence [40], [1], [37], [33].…”

Emergence of coherent wave groups in deep-water random sea

“…Also in this case results are available from both laboratory experiments [25,29] and numerical simulations [15,33,12,28,32,36]. A central finding of such studies consists of the intensification of extreme wave activity for high values of the Benjamin-Feir index (see § 2.1), i.e., when the power spectrum of the surface elevation is sharply peaked around the fundamental wavenumber.…”

“…If extreme waves are to be considered a consequence of breathing modes embedded in a random background [25], then the increased probability of extreme waves for narrowbanded spectra should reflect into a stronger presence of organized structures within the wave field. This is the main point under investigation in this paper, which is organized as follows.…”

Systematic study of rogue wave probability distributions in a fourth‐order nonlinear Schrödinger equation

“…Compared with the observational data [Dankert et al, 2003], the stochastic Rayleigh model greatly underestimates the probability of freak waves. Recent advances in technology have allowed multiple wave tank experiments and field observations to be conducted, confirming the need for a more realistic theory to explain the results [Forristall, 2000;Onorato et al, 2004].…”

“…[3] The scientific community has studied the topic experimentally (in water tanks) [Onorato et al, 2004[Onorato et al, , 2006, observationally (with satellite imaging, for example) [Dankert et al, 2003;Schulz-Stellenfleth and Lehner, 2004], and theoretically [Kharif and Pelinovsky, 2003]. A review of recent progress in freak wave forecasting can be found in an article by Dysthe et al [2008].…”