648 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.
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
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
Low frequency spectra of bending wave turbulence
We study experimentally the dynamics of long waves among turbulent bending
waves in a thin elastic plate set into vibration by a monochromatic forcing at
a frequency . This frequency is chosen large compared with the
characteristic frequencies of bending waves. As a consequence, a range of
conservative scales, without energy flux in average, exists for frequencies
. Within this range, we report a flat power density spectrum for the
orthogonal velocity, corresponding to energy equipartition between modes. Thus,
the average energy per mode -- analogous to a temperature -- fully
characterizes the large-scale turbulent wave field. We present an expression
for as a function of the forcing frequency and amplitude, and of the
plate characteristics
A direct derivation of the Gent-McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics
The transport induced by ocean mesoscale eddies remains unresolved in most
state-of-the-art climate models and needs to be parameterized instead. The
natural scale separation between the forcing and the emergent turbulent flow
calls for a diffusive parameterization, where the eddy-induced fluxes are
related to the large-scale gradients by a diffusion tensor. The standard
parameterization scheme in climate modeling consists in adopting the
Gent-McWilliams/Redi (GM/R) form for the diffusion tensor, initially put
forward based on physical intuition and educated guesses before being put on
firm analytical footing using thickness-weighted average (TWA). In the present
contribution we provide a direct derivation of this diffusion tensor from the
quasi-geostrophic (QG) dynamics of a horizontally homogeneous three-dimensional
patch of ocean hosting a large-scale vertically-sheared zonal flow on the beta
plane. While less general than the TWA approach, the present QG framework leads
to rigorous constraints on the diffusion tensor. First, there is no diapycnal
diffusivity arising in the QG GM/R tensor for low viscosity and small-scale
diffusivities. The diffusion tensor then involves only two vertically dependent
coefficients, namely the GM transport coefficient and the Redi
diffusivity . Secondly, as already identified by previous authors the
vertical structures of the two coefficients are related by the so-called
Taylor-Bretherton relation. Finally, while the two coefficients generically
differ in the interior of the water column, we show that they are equal to one
another near the surface and near the bottom of the domain for low-enough
dissipative coefficients. We illustrate these findings by numerically
simulating the QG dynamics of a horizontally homogeneous patch of ocean hosting
a vertically sheared zonal current resembling the Antarctic Circumpolar
Current
Nouvelles techniques pratiques pour la modélisation du comportement dynamique des systèmes eau-structure
RÉSUMÉ L’´etude des comportements dynamique et sismique des ouvrages hydrauliques est, comme pour les structures conventionnelles, primordiale afin d’assurer la protection des vies humaines. Elle a aussi pour objectif de limiter les dommages structuraux que peut engendrer un tremblement de terre et d’´eviter le cas de rupture ou d’effondrement. Ces structures particulieres subissent non seulement les d´eplacements impos´ees par les secousses sismiques, mais
aussi ceux induits par les forces hydrodynamiques g´en´er´ees par l’interaction fluide-structure. Cette th`ese passe en revue les diff´erentes m´ethodes complexes et simplifi´ees existantes permettant l’analyse dynamique d’ouvrages hydrauliques. En ce qui concerne les m´ethodes complexes,une attention particuli`ere est consacr´ee aux difficult´es li´ees `a leur utilisation. Parmi celles-ci, nous insisterons sur la mod´elisation des conditions aux fronti`eres transmettantes ermettant de simuler num´eriquement l’effet de la g´eom´etrie semi-infinie du r´eservoir. En d´eveloppant une proc´edure pour estimer l’erreur qu’induisent les conditions existantes, nous
montrons que celles-ci peuvent avoir un effet tr`es important sur le comportement dynamique des structures en contact avec de l’eau. Pour les besoins des ing´enieurs-praticiens, des m´ethodes simplifi´ees sont n´ecessaires afin de v´erifier le comportement dynamique des ouvrages en contact avec de l’eau. La revue des m´ethodes simplifi´ees existantes montre que celles-ci sont bas´ees sur de nombreuses simplifications qui peuvent affecter la qualit´e des r´esultats. L’un des objectifs de cette th`ese a ´et´e
de d´evelopper des m´ethodes simplifi´ees plus performantes que celles existantes. Une premi`ere m´ethode a ´et´e mise au point pour la r´ealisation d’une analyse spectrale de ces ouvrages. Pour son d´eveloppement, il a ´et´e n´ecessaire de proposer une m´ethodologie pour le calcul pr´ecis de la p´eriode fondamental d’un syst`eme eau-structure. Nous montrons que cette nouvelle proc´edure est facilement programmable, avec un temps de calcul instantan´e, et que celle-ci donne d’excellents r´esultats lorsque compar´ee `a des m´ethodes complexes.----------ABSTRACT The dynamic or seismic behavior of hydraulic structures is, as for conventional structures, essential to assure protection of human lives. These types of analyses also aim at limiting structural damage caused by an earthquake to prevent rupture or collapse of the structure.
The particularity of these hydraulic structures is that not only the internal displacements are caused by the earthquake, but also by the hydrodynamic loads resulting from fluid-structure interaction. This thesis reviews the existing complex and simplified methods to perform such
dynamic analysis for hydraulic structures. For the complex existing methods, attention is placed on the difficulties arising from their use. Particularly, interest is given in this work on the use of transmitting boundary conditions to simulate the semi infinity of reservoirs. A procedure has been developed to estimate the error that these boundary conditions can introduce in finite element dynamic analysis. Depending on their formulation and location,
we showed that they can considerably affect the response of such fluid-structure systems. For practical engineering applications, simplified procedures are still needed to evaluate the dynamic behavior of structures in contact with water. A review of the existing simplified procedures showed that these methods are based on numerous simplifications that can affect the prediction of the dynamic behavior of such systems. One of the main objectives of this thesis has been to develop new simplified methods that are more accurate than those existing. First, a new spectral analysis method has been proposed. Expressions for the fundamental frequency of fluid-structure systems, key parameter of spectral analysis, have been developed. We show that this new technique can easily be implemented in a spreadsheet or program, and that its calculation time is near instantaneous. When compared to more complex analytical
or numerical method, this new procedure yields excellent prediction of the dynamic behavior of fluid-structure systems
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