Turbulence spectra generated by singularities

Kuznetsov, E. A.

doi:10.1134/1.1804214

Cited by 70 publications

(73 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, the same ω −4 spectrum was predicted by Kuznetsov (Ku) [6] based on the assumption that the dominant contribution to the power-law scaling comes from sharp wave-crests with one-dimensional ridges whose velocity remains nearly constant while crossing the wire probe. Obviously, the nonlinearity of such wave-crests is high and one cannot use the linear dispersion relation for obtaining the space statistics out of the time statistics.…”

Section: Introductionmentioning

confidence: 66%

See 1 more Smart Citation

Statistics of surface gravity wave turbulence in the space and time domains

et al. 2009

View full text Add to dashboard Cite

We present experimental results on simultaneous space-time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as well as with predictions based on the coherent singular wave crests. We see that both wavenumber and the frequency spectra are not universal and dependent on the wave strength, with some evidence in favor of WTT at larger wave intensities when the finite flume effects are minimal. We present further theoretical analysis of the role of the random and coherent waves in the wave probability density function (PDF) and the structure functions (SFs). Analyzing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-gaussian PDF core and in the low-order SFs, and the latter -in the PDF tails and the high-order SF's. It appears that the xspace signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than do the t-space SFs. We outline an approach treating the interactions of these random and coherent components as a turbulence cycle characterized by the turbulence fluxes in both the wavenumber and the amplitude spaces.

show abstract

Section: Introductionmentioning

confidence: 66%

“…Kuznetsov [6] questioned this picture and argued that (i) slope breaks occur on onedimensional lines/ridges rather than on zero-dimensional point/peaks, and (ii) that the wave-crest is propagating with preserved shape, i.e. ω ∝ k should be used instead of the linear wave relation ω = √ gk.…”

Section: Spectramentioning

confidence: 99%

Statistics of surface gravity wave turbulence in the space and time domains

et al. 2009

View full text Add to dashboard Cite

show abstract

“…There is a range of intensities where the PH slope ν = 5 is observed, and we report that wave breaking events were common for such intensities. At higher intensities, one can see the ν = 4 slope which is predicted by both ZF and Kuznetsov theories [3,11]. However, the water surface was visibly very choppy with numerous frequent wavebreaking and high values of the surface slope, γ > 0.15, and rules out the weak nonlinearity assumption which is the basis of ZF theory [3].…”

Section: Spectramentioning

confidence: 94%

“…However, the water surface was visibly very choppy with numerous frequent wavebreaking and high values of the surface slope, γ > 0.15, and rules out the weak nonlinearity assumption which is the basis of ZF theory [3]. Kuznetsov theory [11] is more likely to be relevant to these conditions, because it derives ν = 4 value from considering strongly nonlinear wavecrests with sharp 1D ridges and the speed of which is nearly constant while they pass the height gauge. However, there is no visible plateau in Figure 7 at ν = 4 value and ν takes bigger values at lower intensities and lower values for greater amplitudes (reaching ν = 3.3 for the maximum intensity of γ ≈ 0.21).…”

Section: Spectramentioning

confidence: 99%

See 1 more Smart Citation

Gravity Wave Turbulence in a Laboratory Flume

2007

View full text Add to dashboard Cite

We present experimental results for water wave turbulence excited by piston-like programmed wavemakers in a water flume with dimensions 6 × 12 × 1.5 meters. Our main finding is that for a wide range of excitation amplitudes the energy spectrum has a power-law scaling, E ω ∼ ω −ν . These scalings were achieved in up to one-decade wide frequency range, which is significantly wider than the range available in field observations and in numerical simulations. However, exponent ν appears to be non-universal. It depends on the wavefield intensity and ranges from about 6.5 for weak forcing to about 3.5 for large levels of wave excitations. We discuss our results in the context of the key theoretical predictions, such as Zakharov-Filonenko spectrum ν = −4, Phillips spectrum ν = −5, Kuznetsov's revision of Phillips spectrum (leading to ν = −4) and Nazarenko's prediction ν = −6 for weak turbulence in finite basins. We measured Probability Density Function of the surface elevation and good agreement with the Tayfun shape except values near the maximum which we attribute to an anisotropy and inhomogeneity caused by the finite flume size. We argue that the wavenumber discreteness, due to the finite-size of the flume, prevents four-wave resonant interactions. Therefore, statistical evolution of the water surface in the laboratory is significantly different than in the open ocean conditions.

show abstract

Laboratory study of gravity wave turbulence

Denissenko

Lukaschuk

Nazarenko

Springer Proceedings Physics

View full text Add to dashboard Cite

Turbulence spectra generated by singularities

Cited by 70 publications

References 19 publications

Statistics of surface gravity wave turbulence in the space and time domains

Statistics of surface gravity wave turbulence in the space and time domains

Gravity Wave Turbulence in a Laboratory Flume

Laboratory study of gravity wave turbulence

Contact Info

Product

Resources

About