Effect of discrete resonant manifold structure on discrete wave turbulence

Hrabski, Alexander; Pan, Yulin

doi:10.1103/physreve.102.041101

Cited by 18 publications

(23 citation statements)

References 44 publications

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“…This result is remarkable because of the existence of (sparse) exact resonances for gravity waves on a discrete grid of k (rational torus), in contrast to capillary waves. Before this study it is not clear whether the exact quartet resonances of gravity waves can be connected to result in a cascade (Kartashova, Nazarenko & Rudenko 2008), although this has been demonstrated to be possible in MMT turbulence (Hrabski & Pan 2020). The results here suggest that the energy cascade should not be expected under the current wavenumber range in spite of the existence of energy transfer within a small number of resonant quartets.…”

Section: Energy Fluxmentioning

confidence: 71%

“…With a decrease of nonlinearity level , the power-law spectrum becomes shorter and steeper, reaching α ≈ −3.4 at = 0.068. This steepening of the spectra is in contrast to the results from Majda-McLaughlin-Tabak (MMT) turbulence with ω = k 2 and quartet resonance (Hrabski & Pan 2020), mainly because the latter forms a continuous resonant system (Faou, Germain & Hani 2016) at low nonlinearity (we elaborate this more in § 3.4). We also remark that = 0.151 is about the highest nonlinearity we can reach in the current HOS context.…”

Section: Spectral Slopesmentioning

confidence: 73%

“…In this section, we investigate the scaling between the spectral level of S η (k) and the energy flux P. For the evaluation of P, we can directly compute the energy transfer due to nonlinear terms in the primitive equation (Hrabski & Pan 2020) or use energy dissipation rate as a measure of P (e.g. Pan & Yue 2014).…”

Section: Energy Fluxmentioning

confidence: 99%

“…While all these works report a scaling S η (k) ∼ k −5/2 consistent with (1.1), the simulation (in each of them) is conducted at a single nonlinearity level, and therefore is not capable of resolving/understanding the sensitivity of the spectra to various conditions and their scaling with P. On the other hand, free-decay turbulence is studied for capillary waves in Pan & Yue (2014), which reveals steepened spectra with a decrease of nonlinearity level. However, the finding cannot be naively applied to gravity waves, because the spectral behaviour at low nonlinearity critically depends on the discrete resonant manifold (Hrabski & Pan 2020) which has not been characterized for surface gravity waves.…”

Section: Introductionmentioning

confidence: 99%

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Numerical investigation of turbulence of surface gravity waves

Zhang

Pan

2022

J. Fluid Mech.

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In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and energy flux $P$ at different nonlinearity levels under different forcing/free-decay conditions. For all conditions (free decay and narrow-band and broad-band forcing) that we consider, we find that the spectral forms approach the wave turbulence theory (WTT) solution $S_\eta \sim k^{-5/2}$ and $S_\eta \sim P^{1/3}$ at high nonlinearity levels. With a decrease of nonlinearity level, the spectra for all cases become steeper, with the narrow-band forcing case exhibiting the most rapid deviation from WTT. We investigate bound waves and the finite-size effect as possible mechanisms causing the spectral variations. Through a tri-coherence analysis, we find that the finite-size effect is present in all cases, which is responsible for the overall steepening of the spectra and the reduced capacity of energy flux at lower nonlinearity levels. The fraction of bound waves in the domain generally decreases with the decrease of nonlinearity level, except for the narrow-band case, which exhibits a transition at a critical nonlinearity level below which a rapid increase is observed. This increase serves as the main reason for the fastest deviation from WTT with the decrease of nonlinearity in the narrow-band forcing case.

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Section: Energy Fluxmentioning

confidence: 71%

Section: Spectral Slopesmentioning

confidence: 73%

Section: Energy Fluxmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical investigation of turbulence of surface gravity waves

Zhang

Pan

2022

J. Fluid Mech.

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“…The finite-system size effects are thus more significant when L or P decreases. Taking these effects into account in theories is an important challenge (Zakharov et al 2005, Nazarenko 2006, Kartashova et al 2008, L'vov & Nazarenko 2010, Pan & Yue 2017, Hrabski & Pan 2020.…”

Section: Discreteness Timementioning

confidence: 99%

Experiments in Surface Gravity–Capillary Wave Turbulence

Falcon

Mordant

2022

Annu. Rev. Fluid Mech.

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The last decade has seen a significant increase in the number of studies devoted to wave turbulence. Many deal with water waves, as modeling of ocean waves has historically motivated the development of weak turbulence theory, which addresses the dynamics of a random ensemble of weakly nonlinear waves in interaction. Recent advances in experiments have shown that this theoretical picture is too idealized to capture experimental observations. While gravity dominates much of the oceanic spectrum, waves observed in the laboratory are in fact gravity–capillary waves, due to the restricted size of wave basins. This richer physics induces many interleaved physical effects far beyond the theoretical framework, notably in the vicinity of the gravity–capillary crossover. These include dissipation, finite–system size effects, and finite nonlinearity effects. Simultaneous space-and-time-resolved techniques, now available, open the way for a much more advanced analysis of these effects. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 54 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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Large deviations principle for the cubic NLS equation

Garrido

Grande

Kurianski

et al. 2023

Comm Pure Appl Math

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In this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schrödinger equation on the torus in a weakly nonlinear setting. This equation has been used as a model to numerically study the formation of rogue waves in deep sea. Our results are twofold: first, we introduce a notion of criticality and prove a Large Deviations Principle (LDP) for the subcritical and critical cases. Second, we study the most likely initial conditions that lead to the formation of a rogue wave, from a theoretical and numerical point of view. Finally, we propose several open questions for future research.

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Effect of discrete resonant manifold structure on discrete wave turbulence

Cited by 18 publications

References 44 publications

Numerical investigation of turbulence of surface gravity waves

Numerical investigation of turbulence of surface gravity waves

Experiments in Surface Gravity–Capillary Wave Turbulence

Large deviations principle for the cubic NLS equation

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