102 research outputs found
Intermittency and emergence of coherent structures in wave turbulence of a vibrating plate
We report numerical investigations of wave turbulence in a vibrating plate.
The possibility to implement advanced measurement techniques and long time
numerical simulations makes this system extremely valuable for wave turbulence
studies. The purely 2D character of dynamics of the elastic plate makes it much
simpler to handle compared to much more complex 3D physical systems that are
typical of geo- and astrophysical issues (ocean surface or internal waves,
magnetized plasmas or strongly rotating and/or stratified flows). When the
forcing is small the observed wave turbulence is consistent with the
predictions of the Weak Turbulent Theory. Here we focus on the case of stronger
forcing for which coherent structures can be observed. These structures look
similar to the folds and D-cones that are commonly observed for strongly
deformed static thin elastic sheets (crumpled paper) except that they evolve
dynamically in our forced system. We describe their evolution and show that
their emergence is associated with statistical intermittency (lack of self
similarity) of strongly nonlinear wave turbulence. This behavior is reminiscent
of intermittency in Navier-Stokes turbulence. Experimental data show hints of
the weak to strong turbulence transition. However, due to technical limitations
and dissipation, the strong nonlinear regime remains out of reach of
experiments and therefore has been explored numerically.Comment: accepted for publication in Phys. Rev.
Transition from Weak Wave Turbulence to Soliton-Gas
We report an experimental investigation of the effect of finite depth on the
statistical properties of wave turbulence at the surface of water in the
gravity-capillary range. We tune the wave dispersion and the level of
nonlinearity by modifying the depth of water and the forcing respectively. We
use space-time resolved profilometry to reconstruct the deformed surface of
water. When decreasing the water depth, we observe a drastic transition between
weak turbulence at the weakest forcing and a solitonic regime at stronger
forcing. We characterize the transition between both states by studying their
Fourier Spectra. We also study the efficiency of energy transfer in the weak
turbulence regime. We report a loss of efficiency of angular transfer as the
dispersion of the wave is reduced until the system bifurcates into the
solitonic regime.Comment: published in Physical Review Fluid
Nonlocal resonances in weak turbulence of gravity-capillary waves
We report a laboratory investigation of weak turbulence of water surface
waves in the gravity-capillary crossover. By using time-space resolved
profilometry and a bicoherence analysis, we observe that the nonlinear
processes involve 3-wave resonant interactions. By studying the solutions of
the resonance conditions we show that the nonlinear interaction is dominantly
1D and involves collinear wave vectors. Furthermore taking into account the
spectral widening due to weak nonlinearity explains that nonlocal interactions
are possible between a gravity wave and high frequency capillary ones. We
observe also that nonlinear 3-wave coupling is possible among gravity waves and
we raise the question of the relevance of this mechanism for oceanic waves.Comment: accepted for publication in Physical Review Letter
The role of dissipation in flexural wave turbulence: from experimental spectrum to Kolmogorov-Zakharov spectrum
The Weak Turbulence Theory has been applied to waves in thin elastic plates
obeying the F\"oppl-Von K\'arm\'an dynamical equations. Subsequent experiments
have shown a strong discrepancy between the theoretical predictions and the
measurements. Both the dynamical equations and the Weak Turbulence Theory
treatment require some restrictive hypotheses. Here a direct numerical
simulation of the F\"oppl-Von K\'arm\'an equations is performed and reproduces
qualitatively and quantitatively the experimental results when the
experimentally measured damping rate of waves is
used. This confirms that the F\"oppl-Von K\'arm\'an equations are a valid
theoretical framework to describe our experiments. When we progressively tune
the dissipation so that to localize it at the smallest scales, we observe a
gradual transition between the experimental spectrum and the
Kolmogorov-Zakharov prediction. Thus it is shown dissipation has a major
influence on the scaling properties stationary solutions of weakly non linear
wave turbulence.Comment: 10 pages, 11 figure
Wave turbulence buildup in a vibrating plate
We report experimental and numerical results on the buildup of the energy
spectrum in wave turbulence of a vibrating thin elastic plate. Three steps are
observed: first a short linear stage, then the turbulent spectrum is
constructed by the propagation of a front in wave number space and finally a
long time saturation due to the action of dissipation. The propagation of a
front at the second step is compatible with scaling predictions from the Weak
Turbulence Theory.Comment: accepted for publication in European Physical Journal
Transition from wave turbulence to dynamical crumpling in vibrated elastic plates
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.Comment: accepted for publication in Physical Review Letter
Experiments in Surface Gravity-Capillary Wave Turbulence
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 adresses 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.Comment: Preprint version. Posted with permission from the Annual Review of
fluid Mechanics, Volume 54, copyright 2022 Annual Reviews,
https://www.annualreviews.org
Nonlinear dynamics of flexural wave turbulence
The Kolmogorov-Zakharov spectrum predicted by the Weak Turbulence Theory
remains elusive for wave turbulence of flexural waves at the surface of an thin
elastic plate. We report a direct measurement of the nonlinear timescale
related to energy transfer between waves. This time scale is extracted
from the space-time measurement of the deformation of the plate by studying the
temporal dynamics of wavelet coefficients of the turbulent field. The central
hypothesis of the theory is the time scale separation between dissipative time
scale, nonlinear time scale and the period of the wave (). We
observe that this scale separation is valid in our system. The discrete modes
due to the finite size effects are responsible for the disagreement between
observations and theory. A crossover from continuous weak turbulence and
discrete turbulence is observed when the nonlinear time scale is of the same
order of magnitude as the frequency separation of the discrete modes. The
Kolmogorov-Zakharov energy cascade is then strongly altered and is frozen
before reaching the dissipative regime expected in the theory.Comment: accepted for publication in Physical Review
Confinement effects on gravity-capillary wave turbulence
The statistical properties of a large number of weakly nonlinear waves can be
described in the framework of the Weak Turbulence Theory. The theory is based
on the hypothesis of an asymptotically large system. In experiments, the
systems have a finite size and the predictions of the theory may not apply
because of the presence of discrete modes rather than a continuum of free
waves. Our study focusses on the case of waves at the surface of water at
scales close to the gravity-capillarity crossover (of order 1~cm). Wave
turbulence has peculiar properties in this regime because 1D resonant
interactions can occur as shown by Aubourg \& Mordant. Here we investigate the
influence of the confinement on the properties of wave turbulence by reducing
gradually the size of our wave tank along one of its axis, the size in the
other direction being unchanged. We use space-time resolved profilometry to
reconstruct the deformed surface of water. We observe an original regime of
coexistence of weak wave turbulence along the length of the vessel and discrete
turbulence in the confined direction.Comment: accepted for publication in Physical Review Fluid
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