Wave Turbulence: A Story Far from Over

Newell, Alan C.; Rumpf, Benno

doi:10.1142/9789814366946_0001

Cited by 14 publications

(14 citation statements)

References 88 publications

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“…">1.The Phillips' spectrum

n_{k} = C g^{1 / 2} k^{- 9 / 2}

is the only spectrum for which

\frac{t_{L}}{t_{N L}}

is independent of both k and P . C is a pure constant, which is estimated to be about 1/25 from the data quoted in Newell and Zakharov , and Newell and Rumpf . 2.The breakdown wavenumber

k_{1} = \frac{g}{P^{2 / 3}}

is the wavenumber at which the KZ spectrum

n_{k} = P^{1 / 3} k^{- 4}

and the Phillips' spectrum

n_{k} = C g^{1 / 2} k^{- 9 / 2}

intersect. …”

Section: The Statistically Steady State Of a Developed Seamentioning

confidence: 99%

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Whitecapping

Dyachenko

Newell

2016

Stud Appl Math

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The work we describe addresses the process of whitecapping. We first argue that, when the winds are strong enough, the ocean surface must develop an alternative means to dissipate energy when its flux from large to small scales becomes too large. We then show that the resulting Phillips' spectrum, which holds at small or meter length scales, is dominated by sharp crested waves. We next idealize such a sea locally by a family of close to maximum amplitude Stokes waves and show, using highly accurate simulation algorithms based on a conformal map representation, that perturbed Stokes waves develop the universal feature of an overturning plunging jet. We analyze both the cases when surface tension is absent and present. In the latter case, we show the plunging jet is regularized by capillary waves that rapidly become nonlinear Crapper waves in whose trough pockets whitecaps may be spawned. We are careful not to claim this as the definitive mechanism for whitecaps because three-dimensional effects, although qualitatively discussed, are not included in the analysis.

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“…">1.The Phillips' spectrum

n_{k} = C g^{1 / 2} k^{- 9 / 2}

is the only spectrum for which

\frac{t_{L}}{t_{N L}}

is independent of both k and P . C is a pure constant, which is estimated to be about 1/25 from the data quoted in Newell and Zakharov , and Newell and Rumpf . 2.The breakdown wavenumber

k_{1} = \frac{g}{P^{2 / 3}}

is the wavenumber at which the KZ spectrum

n_{k} = P^{1 / 3} k^{- 4}

and the Phillips' spectrum

n_{k} = C g^{1 / 2} k^{- 9 / 2}

intersect. …”

Section: The Statistically Steady State Of a Developed Seamentioning

confidence: 99%

“…) over large spectral ranges. However, they are not uniformly valid in wavenumber because they do not keep the ratio of linear

t_{L} = ω^{- 1}

to nonlinear timescales

t_{N L} = \frac{1}{n_{k}} \frac{d n_{k}}{d t}

uniformly small for all k , a necessary condition for the validity of the wave turbulence closure .…”

Section: The Statistically Steady State Of a Developed Seamentioning

confidence: 99%

Whitecapping

Dyachenko

Newell

2016

Stud Appl Math

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“…There are several formulations of the closure hypothesis which are essentially equivalent (e.g. Benney & Saffman, 1966;Zakharov et al, 1992;Nazarenko, 2011;Newell & Rumpf, 2013).…”

Section: Basic Equationsmentioning

confidence: 99%

“…Simulations of waves without energy input (swell), which are of primary interest for us, have received relatively little attention (see Badulin & Zakharov, 2017, and references therein). The KE is based on two key assumptions: the statistical closure, often referred to as "the natural" closure (since it naturally occurs as a result of an asymptotic procedure based on small nonlinearity for broadband wave fields under the presumed absence of coherent patterns (Newell & Rumpf, 2013)), and the quasi-stationarity, implied by the large-time limit taken to obtain the solution for the fourth-order cumulant (Zakharov et al, 1992;. The behaviour of discrepancies between the kinetic theory and the reality, as well as the specific role of each of these assumptions, are not clear yet.…”

Section: Introductionmentioning

confidence: 99%

Spectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulations

Annenkov

Shrira

2018

J. Fluid Mech.

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Kinetic equations are widely used in many branches of science to describe the evolution of random wave spectra. To examine the validity of these equations, we study numerically the long-term evolution of water wave spectra without wind input using three different models. The first model is the classical kinetic (Hasselmann) equation (KE). The second model is the generalised kinetic equation (gKE), derived employing the same statistical closure as the KE but without the assumption of quasistationarity. The third model, which we refer to as the DNS-ZE, is a direct numerical simulation algorithm based on the Zakharov integrodifferential equation, which plays the role of the primitive equation for a weakly nonlinear wave field. It does not employ any statistical assumptions. We perform a comparison of the spectral evolution of the same initial distributions without forcing, with/without a statistical closure and with/without the quasistationarity assumption. For the initial conditions, we choose two narrow-banded spectra with the same frequency distribution and different degrees of directionality. The short-term evolution ($O(10^{2})$ wave periods) of both spectra has been previously thoroughly studied experimentally and numerically using a variety of approaches. Our DNS-ZE results are validated both with existing short-term DNS by other methods and with available laboratory observations of higher-order moment (kurtosis) evolution. All three models demonstrate very close evolution of integral characteristics of the spectra, approaching with time the theoretical asymptotes of the self-similar stage of evolution. Both kinetic equations give almost identical spectral evolution, unless the spectrum is initially too narrow in angle. However, there are major differences between the DNS-ZE and gKE/KE predictions. First, the rate of angular broadening of initially narrow angular distributions is much larger for the gKE and KE than for the DNS-ZE, although the angular width does appear to tend to the same universal value at large times. Second, the shapes of the frequency spectra differ substantially (even when the nonlinearity is decreased), the DNS-ZE spectra being wider than the KE/gKE ones and having much lower spectral peaks. Third, the maximal rates of change of the spectra obtained with the DNS-ZE scale as the fourth power of nonlinearity, which corresponds to the dynamical time scale of evolution, rather than the sixth power of nonlinearity typical of the kinetic time scale exhibited by the KE. The gKE predictions fall in between. While the long-term DNS show excellent agreement with the KE predictions for integral characteristics of evolving wave spectra, the striking systematic discrepancies for a number of specific spectral characteristics call for revision of the fundamentals of the wave kinetic description.

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“…Nowadays, wave turbulence is a vibrant area of research in nonlinear wave theory with important practical applications in several areas including oceanography and plasma physics, to mention a few. We refer to [31,32] for recent reviews.…”

Section: Introductionmentioning

confidence: 99%