Linking Reduced Breaking Crest Speeds to Unsteady Nonlinear Water Wave Group Behavior

Banner, Michael L.; Barthelemy, Xavier; Fedele, Francesco; Allis, Michael; Benetazzo, Alvise; Dias, Frédéric; Peirson, William L.

doi:10.1103/physrevlett.112.114502

Cited by 76 publications

(80 citation statements)

References 24 publications

(14 reference statements)

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“…Note that in oceanic wave groups, large focusing crests tend to slow down as they evolve within the group, as a result of the natural wave dispersion of unsteady wave trains (Banner et al 2014;Fedele 2014a,b). Thus, we argue that the observed slowdown of the passive scalar peaks may be due to the wave-like dispersive nature of small-scale turbulent structures.…”

Section: Discussionmentioning

confidence: 98%

Symmetry reduction of turbulent pipe flows

2015

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We propose and apply a Fourier-based symmetry reduction scheme to remove, or quotient, the streamwise translation symmetry of Laser-Induced-Fluorescence measurements of turbulent pipe flows that are viewed as dynamical systems in a high-dimensional state space. We also explain the relation between Taylor's hypothesis and the comoving frame velocity $U_{d}$ of the turbulent orbit in state space. In particular, in physical space we observe flow structures that deform as they advect downstream at a speed that differs significantly from $U_{d}$. Indeed, the symmetry reduction analysis of planar dye concentration fields at Reynolds number $\mathfrak{\mathsf{Re}}=3200$ reveals that the speed $u$ at which high concentration peaks advect is roughly 1.43 times $U_{d}$. In a physically meaningful symmetry-reduced frame, the excess speed $u-U_{d}\approx0.43U_{d}$ can be explained in terms of the so-called geometric phase velocity $U_{g}$ associated with the orbit in state space. The 'self-propulsion velocity' $U_{g}$ is induced by the shape-changing dynamics of passive scalar structures observed in the symmetry-reduced frame, in analogy with that of a swimmer at low Reynolds numbers.Comment: arXiv admin note: substantial text overlap with arXiv:1407.748

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Section: Discussionmentioning

confidence: 98%

Symmetry reduction of turbulent pipe flows

2015

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“…Furthermore, smaller crests span the entire range of positions within the group, but large waves, including rogue waves, are concentrated near the center (Figures c and g). This is consistent with the complex growth behavior of nonbreaking crests within wave groups, where faster waves, moving toward the front of the group, are associated with decreasing height [ Banner et al , ].…”

Section: Asymmetry Of Wave Groupsmentioning

confidence: 96%

Observations of the shape and group dynamics of rogue waves

Gemmrich

Thomson

2017

Geophysical Research Letters

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Surface elevation records from two locations in the northeast Pacific are used to examine rogue waves and the relationship to wave groups. Three hundred individual rogue waves with heights greater than 2.2 times the significant wave height are found in analyzing >2 × 106 wave groups. In contrast to recent nonlinear modeling results, we do not find that rogue waves occur at the front of wave groups. There is a tendency for steep waves to occur at the front of a group, but these are not the largest waves of the group and do not meet the rogue wave criterion. Rogue waves are most commonly located in the center of the group, but their height ratio to the neighboring crest is greater than in the average wave group. Assessing group dynamics in terms of spectral width suggests that random superposition of nonlinear waves is sufficient to explain the observations of individual rogue waves.

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“…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).…”

Section: Introductionmentioning

confidence: 99%

Observation of Extreme Sea Waves in a Space–Time Ensemble

Benetazzo

Barbariol

Bergamasco

et al. 2015

Journal of Physical Oceanography

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In this paper, an observational space-time ensemble of sea surface elevations is investigated in search of the highest waves of the sea state. Wave data were gathered by means of a stereo camera system, which was installed on top of a fixed oceanographic platform located in the Adriatic Sea (Italy). Waves were measured during a mature sea state with an average wind speed of 11 m s 21 . By examining the space-time ensemble, the 3D wave groups have been isolated while evolving in the 2D space and grabbed ''when and where'' they have been close to the apex of their development, thus exhibiting large surface displacements. The authors have selected the groups displaying maximal crest height exceeding the threshold adopted to define rogue waves in a time record, that is, 1.25 times the significant wave height (H s ). The records at the spatial positions where such large crests occurred have been analyzed to derive the empirical distributions of crest and wave heights, which have been compared against standard statistical linear and nonlinear models. Here, the maximal observed wave crests have resulted to be outliers of the standard statistics, behaving as isolated members of the sample, apparently uncorrelated with other waves of the record. However, this study has found that these unexpectedly large wave crests are better approximated by a space-time model for extreme crest heights. The space-time model performance has been improved, deriving a second-order approximation of the linear model, which has provided a fair agreement with the empirical maxima. The present investigation suggests that very large waves may be more numerous than generally expected.

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Linking Reduced Breaking Crest Speeds to Unsteady Nonlinear Water Wave Group Behavior

Cited by 76 publications

References 24 publications

Symmetry reduction of turbulent pipe flows

Symmetry reduction of turbulent pipe flows

Observations of the shape and group dynamics of rogue waves

Observation of Extreme Sea Waves in a Space–Time Ensemble

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