Crest speeds of unsteady surface water waves

Fedele, Francesco; Banner, Michael L.; Barthelemy, Xavier

doi:10.1017/jfm.2020.424

Cited by 8 publications

(27 citation statements)

References 81 publications

(157 reference statements)

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“…Derakhti et al. 2020; Fedele, Banner & Barthelemy 2020) does lead to a level of uncertainty in the resultant time-series. This is managed by filtering the data with a running mean of width , which we find effectively removes high-frequency noise without significantly smoothing the temporal variability in the data.…”

Section: Methodsmentioning

confidence: 99%

“…Cubic interpolation is used to determine the location of x + and the value of the energetic quantities at this point, but the unsteady movement of the crest (e.g. Derakhti et al 2020;Fedele, Banner & Barthelemy 2020) does lead to a level of uncertainty in the resultant time-series. This is managed by filtering the data with a running mean of width 0.15T p , which we find effectively removes high-frequency noise without significantly smoothing the temporal variability in the data.…”

Section: The Crest Ensemblementioning

confidence: 99%

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An energetic signature for breaking inception in surface gravity waves

et al. 2023

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A dynamical understanding of the physical process of surface gravity wave breaking remains an unresolved problem in fluid dynamics. Conceptually, breaking can be described by inception and onset, where breaking inception is the initiation of unknown irreversible processes within a wave crest that precede the visible manifestation of breaking onset. In the search for an energetic indicator of breaking inception, we use an ensemble of non-breaking and breaking crests evolving within unsteady wave packets simulated in a numerical wave tank to investigate the evolution of each term in the kinetic energy balance equation. We observe that breaking onset is preceded by around one quarter of a wave period by a rapid increase in the rate of convergence of kinetic energy that triggers an irreversible acceleration of the kinetic energy growth rate. This energetic signature, which is present only for crests that subsequently break, arises when the kinetic energy growth rate exceeds a critical threshold. At this point the additional kinetic energy convergence cannot be offset by converting excess kinetic energy to potential energy or by dissipation through friction. Our results suggest that the ratio of the leading terms of the kinetic energy balance equation at the time of this energetic signature is proportional to the strength of the breaking crest. Hence this energetic inception point both predicts the occurrence of breaking onset and indicates the strength of the breaking event.

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Section: Methodsmentioning

confidence: 99%

Section: The Crest Ensemblementioning

confidence: 99%

An energetic signature for breaking inception in surface gravity waves

et al. 2023

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“…Studies such as these have identified the main controlling parameters of breaking waves, namely the breaking speed and the wave slope at breaking S = ak, where a is the wave amplitude, and k is the wavenumber. The bandwidth of the wave packet is also important, and the detailed kinematics before breaking, in particular a significant slowdown of the wave crest, have been discussed in order to propose breaking threshold criteria (Banner et al 2014;Saket et al 2017;Derakhti et al 2020;Fedele et al 2020), although we will neglect its influence from here onwards.…”

Section: Laboratory Experiments and Direct Numerical Simulations Of C...mentioning

confidence: 99%

“…As wave energy focuses through linear or nonlinear processes, local conditions on a wave surface become unstable and cause breaking, which transfers energy and momentum to the water column. The geometry and kinematics of the breaking waves have been studied extensively (Longuet-Higgins & Cokelet 1976;Perlin, Choi & Tian 2013;Schwendeman & Thomson 2017;Fedele, Banner & Barthelemy 2020), and the identification of a breaking threshold with approaches based on the wave kinematics, dynamics or geometry remains a longstanding issue (Melville 1982;Banner & Peirson 2007;Perlin et al 2013), with recent work discussing the link between the breaker kinematics and dynamics (Saket et al 2017;Derakhti et al 2020;Pizzo 2020).…”

Section: The Broader Contextmentioning

confidence: 99%

High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplets production

2022

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We present high-resolution three-dimensional (3-D) direct numerical simulations of breaking waves solving for the two-phase Navier–Stokes equations. We investigate the role of the Reynolds number (Re, wave inertia relative to viscous effects) and Bond number (Bo, wave scale over the capillary length) on the energy, bubble and droplet statistics of strong plunging breakers. We explore the asymptotic regimes at high Re and Bo, and compare with laboratory breaking waves. Energetically, the breaking wave transitions from laminar to 3-D turbulent flow on a time scale that depends on the turbulent Re up to a limiting value $Re_\lambda \sim 100$ , consistent with the mixing transition in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process, and extend the buoyant-energetic scaling from Deike et al. (J. Fluid Mech., vol. 801, 2016, pp. 91–129) to account for the cavity shape and its scale separation from the Hinze scale, $r_H$ . We confirm two regimes in the bubble size distribution, $N(r/r_H)\propto (r/r_H)^{-10/3}$ for $r>r_H$ , and $\propto (r/r_H)^{-3/2}$ for $r<r_H$ . Bubbles are resolved up to one order of magnitude below $r_H$ , and we observe a good collapse of the numerical data compared to laboratory breaking waves (Deane & Stokes, Nature, vol. 418 (6900), 2002, pp. 839–844). We resolve droplet statistics at high Bo in good agreement with recent experiments (Erinin et al., Geophys. Res. Lett., vol. 46 (14), 2019, pp. 8244–8251), with a distribution shape close to $N_d(r_d)\propto r_d^{-2}$ . The evolution of the droplet statistics appears controlled by the details of the impact process and subsequent splash-up. We discuss velocity distributions for the droplets, finding ejection velocities up to four times the phase speed of the wave, which are produced during the most intense splashing events of the breaking process.

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“…Nevertheless, Stansell & MacFarlane (2002) questioned the physical significance of phase reversal effect emphasised by Melville (1983) (reduction of the local phase speed below zero), as it can be subject to the peculiarity of Hilbert transform. On the other hand, Banner et al (2014), Fedele, Chandre & Farazmand (2016 and Fedele, Banner & Barthelemy (2020) showed that the crest speed of a nearly breaking wave can significantly deviate from the phase speed suggested by both (2.13) and (4.16). The actual wave crest speed exhibits very fast variations: whether a crest experiences slowing down or speeding up depends on the dispersion regime it belongs to.…”

Section: Dispersion Variationmentioning

confidence: 88%

On an eddy viscosity model for energetic deep-water surface gravity wave breaking

Khait

2021

J. Fluid Mech.

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We present an investigation of the fundamental physical processes involved in deep-water gravity wave breaking. Our motivation is to identify the underlying reason causing the deficiency of the eddy viscosity breaking model (EVBM) in predicting surface elevation for strongly nonlinear waves. Owing to the limitation of experimental methods in the provision of high-resolution flow information, we propose a numerical methodology by developing an EVBM enclosed standalone fully nonlinear quasi-potential (FNP) flow model and a coupled FNP plus Navier–Stokes flow model. The numerical models were firstly verified with a wave train subject to modulational instability, then used to simulate a series of broad-banded focusing wave trains under non-, moderate- and strong-breaking conditions. A systematic analysis was carried out to investigate the discrepancies of numerical solutions produced by the two models in surface elevation and other important physical properties. It is found that EVBM predicts accurately the energy dissipated by breaking and the amplitude spectrum of free waves in terms of magnitude, but fails to capture accurately breaking induced phase shifting. The shift of phase grows with breaking intensity and is especially strong for high-wavenumber components. This is identified as a cause of the upshift of the wave dispersion relation, which increases the frequencies of large-wavenumber components. Such a variation drives large-wavenumber components to propagate at nearly the same speed, which is significantly higher than the linear dispersion levels. This suppresses the instant dispersive spreading of harmonics after the focal point, prolonging the lifespan of focused waves and expanding their propagation space.

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Crest speeds of unsteady surface water waves

Abstract: Abstract

Cited by 8 publications

References 81 publications

An energetic signature for breaking inception in surface gravity waves

An energetic signature for breaking inception in surface gravity waves

High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplets production

On an eddy viscosity model for energetic deep-water surface gravity wave breaking

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