Space-Time Resolved Wave Turbulence in a Vibrating Plate

Cobelli, Pablo; Petitjeans, Philippe; Maurel, Agnès; Pagneux, Vincent; Mordant, Nicolas

doi:10.1103/physrevlett.103.204301

Cited by 61 publications

(84 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2.1) and (2.2) are related through the dispersion relation ω = W (k). This has been checked only recently by comparison of the spatial and temporal spectra determined in experiments of waves on elastic plates (Cobelli et al, 2009) and capillary-gravity surface waves (Snouck et al, 2009;Herbert et al, 2010). A fair agreement has been found in the former case whereas a more complex structure in the spatio-temporal domain exists in the latter ones.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations of Energy Flux in Wave Turbulence

et al. 2008

View full text Add to dashboard Cite

The key governing parameter of wave turbulence is the energy flux that drives the waves and cascades to small scales through nonlinear interactions. In the inertial range, the energy flux is conserved across the scales, and is assumed to be constant in most theoretical approaches. It is only recently that measurements of the injected power into wave turbulence have been performed at the scale of the wave maker (integral scale). In this review, we focus on the statistical properties of the injected power fluctuations in gravity-capillary wave turbulence in a stationary regime. Fluctuations of the injected power have been found much larger than their mean value. In addition, events related to a negative injected power, i.e. an instantaneous reversed energy flux, occur with a fairly large probability. Both features are well described using a Langevin type equation. Finally, we consider the experimental dependence of the scaling law of the wave spectrum with the mean injected power and discuss possible reasons for the discrepancy with weak turbulence theory.

show abstract

Section: Introductionmentioning

confidence: 99%

Fluctuations of Energy Flux in Wave Turbulence

et al. 2008

View full text Add to dashboard Cite

show abstract

“…The forcing intensity is tuned by changing the amplitude of the excitation. The deformation of the plate is measured using a high speed Fourier transform profilometry technique [7,20] providing movies of the deformation over about 1 m 2 (i.e. half the total surface of the plate) that are resolved both in time and space.…”

mentioning

confidence: 99%

Transition from Wave Turbulence to Dynamical Crumpling in Vibrated Elastic Plates

et al. 2013

Self Cite

View full text Add to dashboard Cite

We study the dynamical regime of wave turbulence of a vibrated thin elastic plate based on experimental and numerical observations. We focus our study to the strongly non linear regime described in a previous letter by N. Yokoyama & M. Takaoka. At small forcing, a weakly non linear regime is compatible with the Weak Turbulence Theory when the dissipation is localized at high wavenumber. When the forcing intensity is increased, a strongly non linear regime emerges: singular structures dominate the dynamics at large scale whereas at small scales the weak turbulence is still present. A turbulence of singular structures, with folds and D-cones, develops that alters significantly the energy spectra and causes the emergence of intermittency.

show abstract

“…The elastic-wave turbulence, which is tractable experimentally, numerically and theoretically, exhibits rich phenomena: weak turbulence [12,18], spatio-temporal dynamics [19], spectral variation [7,20] and strongly nonlinear structures [21]. Among them, the coexistence of the weakly nonlinear spectrum and a strongly nonlinear spectrum is one of the most remarkable properties [7,22].…”

Section: Introductionmentioning

confidence: 99%

Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl–von Kármán equation: Energy decomposition analysis and energy budget

Yokoyama

Takaoka

2014

Phys. Rev. E

View full text Add to dashboard Cite

A single-wavenumber representation of nonlinear energy spectrum, i.e., stretching energy spectrum is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wavenumber space, and analytical expressions of detailed energy budget in the nonlinear interactions are obtained for the first time in wave turbulence systems. We numerically solved the FvK equation and observed the following facts. Kinetic and bending energies are comparable with each other at large wavenumbers as the weak turbulence theory suggests. On the other hand, the stretching energy is larger than the bending energy at small wavenumbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a k and its companion mode a −k is observed at the small wavenumbers. Energy transfer shows that the energy is input into the wave field through stretching-energy transfer at the small wavenumbers, and dissipated through the quartic part of kinetic-energy transfer at the large wavenumbers. A total-energy flux consistent with the energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.

show abstract

Space-Time Resolved Wave Turbulence in a Vibrating Plate

Cited by 61 publications

References 19 publications

Fluctuations of Energy Flux in Wave Turbulence

Fluctuations of Energy Flux in Wave Turbulence

Transition from Wave Turbulence to Dynamical Crumpling in Vibrated Elastic Plates

Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl–von Kármán equation: Energy decomposition analysis and energy budget

Contact Info

Product

Resources

About