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Author (up) During, G.; Josserand, C.; Krstulovic, G.; Rica, S.
Title Strong turbulence for vibrating plates: Emergence of a Kolmogorov spectrum Type
Year 2019 Publication Physical Review Fluids Abbreviated Journal Phys. Rev. Fluids
Volume 4 Issue 6 Pages 12 pp
Keywords
Abstract In fluid turbulence, energy is transferred from one scale to another by an energy cascade that depends only on the energy-dissipation rate. It leads by dimensional arguments to the Kolmogorov 1941 (K41) spectrum. Here we show that the normal modes of vibrations in elastic plates also manifest an energy cascade with the same K41 spectrum in the fully nonlinear regime. In particular, we observe different patterns in the elastic deformations such as folds, developable cones, and even more complex stretching structures, in analogy with spots, swirls, vortices, and other structures in hydrodynamic turbulence. We show that the energy cascade is dominated by the kinetic contribution and that the stretching energy is at thermodynamical equilibrium. We characterize this energy cascade, the validity of the constant energy-dissipation rate over the scales. Finally, we discuss the role of intermittency using the correlation functions that exhibit anomalous exponents.
Address [During, Gustavo] Pontificia Univ Catolica Chile, Inst Fis, Casilla 306, Santiago, Chile, Email: sergio.rica@uai.cl
Corporate Author Thesis
Publisher Amer Physical Soc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2469-990x ISBN Medium
Area Expedition Conference
Notes WOS:000471999200003 Approved
Call Number UAI @ eduardo.moreno @ Serial 1025
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Author (up) During, G.; Josserand, C.; Rica, S.
Title Wave turbulence theory of elastic plates Type
Year 2017 Publication Physica D-Nonlinear Phenomena Abbreviated Journal Physica D
Volume 347 Issue Pages 42-73
Keywords Wave turbulence; Elastic plates; Kinetic equation; Numerical simulations
Abstract This article presents the complete study of the long-time evolution of random waves of a vibrating thin elastic plate in the limit of small plate deformation so that modes of oscillations interact weakly. According to the wave turbulence theory a nonlinear wave system evolves in longtime creating a slow redistribution of the spectral energy from one mode to another. We derive step by step, following the method of cumulants expansion and multiscale asymptotic perturbations, the kinetic equation for the second order cumulants as well as the second and fourth order renormalization of the dispersion relation of the waves. We characterize the non-equilibrium evolution to an equilibrium wave spectrum, which happens to be the well known Rayleigh-Jeans distribution. Moreover we show the existence of an energy cascade, often called the Kolmogorov-Zakharov spectrum, which happens to be not simply a power law, but a logarithmic correction to the Rayleigh Jeans distribution. We perform numerical simulations confirming these scenarii, namely the equilibrium relaxation for closed systems and the existence of an energy cascade wave spectrum. Both show a good agreement between theoretical predictions and numerics. We show also some other relevant features of vibrating elastic plates, such as the existence of a self-similar wave action inverse cascade which happens to blow-up in finite time. We discuss the mechanism of the wave breakdown phenomena in elastic plates as well as the limit of strong turbulence which arises as the thickness of the plate vanishes. Finally, we discuss the role of dissipation and the connection with experiments, and the generalization of the wave turbulence theory to elastic shells. (C) 2017 Elsevier B.V. All rights reserved.
Address [During, Gustavo] Pontificia Univ Catolica Chile, Fac Fis, Casilla 306, Santiago, Chile, Email: christophe.josserand@upmc.fr
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0167-2789 ISBN Medium
Area Expedition Conference
Notes WOS:000399856000004 Approved
Call Number UAI @ eduardo.moreno @ Serial 728
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Author (up) During, G.; Josserand, C.; Rica, S.
Title Self-similar formation of an inverse cascade in vibrating elastic plates Type
Year 2015 Publication Physical Review E Abbreviated Journal Phys. Rev. E
Volume 91 Issue 5 Pages 10 pp
Keywords
Abstract The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a time-dependent inverse cascade, opening up the possibility of self-organization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the short-wave fluctuations. This dynamics appears to be self-similar and possesses a power-law behavior in the short-wavelength limit which significantly differs from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a long-wave coherent structure in finite time.
Address [Duering, Gustavo] Pontificia Univ Catolica Chile, Fac Fis, Santiago, Chile
Corporate Author Thesis
Publisher Amer Physical Soc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2470-0045 ISBN Medium
Area Expedition Conference
Notes WOS:000354983600007 Approved
Call Number UAI @ eduardo.moreno @ Serial 493
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Author (up) Humbert, T.; Cadot, O.; During, G.; Josserand, C.; Rica, S.; Touze, C.
Title Wave turbulence in vibrating plates: The effect of damping Type
Year 2013 Publication Epl Abbreviated Journal Epl
Volume 102 Issue 3 Pages 6 pp
Keywords
Abstract The effect of damping in the wave turbulence regime for thin vibrating plates is studied. An experimental method, allowing measurements of dissipation in the system at all scales, is first introduced. Practical experimental devices for increasing the dissipation are used. The main observable consequence of increasing the damping is a significant modification in the slope of the power spectral density, so that the observed power laws are not in a pure inertial regime. However, the system still displays a turbulent behavior with a cut-off frequency that is determined by the injected power which does not depend on damping. By using the measured damping power-law in numerical simulations, similar conclusions are drawn out. Copyright (C) EPLA, 2013
Address Univ Paris 06, CNRS, UMR 7190, Inst Alembert, F-75005 Paris, France
Corporate Author Thesis
Publisher Epl Association, European Physical Society Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0295-5075 ISBN Medium
Area Expedition Conference
Notes WOS:000319697000002 Approved
Call Number UAI @ eduardo.moreno @ Serial 283
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Author (up) Josserand, C.; Pomeau, Y.; Rica, S.
Title Finite-time localized singularities as a mechanism for turbulent dissipation Type
Year 2020 Publication Physical Review Fluids Abbreviated Journal Phys. Rev. Fluids
Volume 5 Issue 5 Pages 15 pp
Keywords
Abstract The nature of the fluctuations of the dissipation rate in fluid turbulence is still under debate. One reason may be that the observed fluctuations are strong events of dissipation, which reveal the trace of spatiotemporal singularities of the Euler equations, which are the zero viscosity limit of ordinary incompressible fluids. Viscosity regularizes these hypothetical singularities, resulting in a chaotic fluctuating state in which the strong events appear randomly in space and time, making the energy dissipation highly fluctuating. Yet, to date, it is not known if smooth initial conditions of the Euler equations with finite energy do or do not blow up in finite time. We overcome this central difficulty by providing a scenario for singularity-mediated turbulence based on the self-focusing nonlinear Schrodinger equation. It avoids the intrinsic difficulty of Euler equations since it is well known that solutions of this NLS equation with smooth initial conditions do blow up in finite time. When adding viscosity, the model shows (i) that dissipation takes place near the singularities only, (ii) that such intense events are random in space and time, (iii) that the mean dissipation rate is almost constant as the viscosity varies, and (iv) the observation of an Obukhov-Kolmogorov spectrum with a power-law dependence together with an intermittent behavior using structure function correlations, in close correspondence with the one measured in fluid turbulence.
Address [Josserand, Christophe; Pomeau, Yves; Rica, Sergio] CNRS, LadHyX, F-91128 Palaiseau, France, Email: sergio.rica@uai.cl
Corporate Author Thesis
Publisher Amer Physical Soc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 2469-990x ISBN Medium
Area Expedition Conference
Notes WOS:000535862800004 Approved
Call Number UAI @ eduardo.moreno @ Serial 1198
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Author (up) Mason, P.; Josserand, C.; Rica, S.
Title Activated Nucleation of Vortices in a Dipole-Blockaded Supersolid Condensate Type
Year 2012 Publication Physical Review Letters Abbreviated Journal Phys. Rev. Lett.
Volume 109 Issue 4 Pages 5 pp
Keywords
Abstract We investigate theoretically and numerically a model of a supersolid in a dipole-blockaded Bose-Einstein condensate. The dependence of the superfluid fraction with an imposed thermal bath and a uniform boost velocity on the condensate is considered. Specifically, we observe a critical velocity for the nucleation of vortices in our system that is strongly linked to a steplike decrease in the superfluid fraction. We are able to use a scaling argument based on the energy required to activate a vortex, relating the critical temperature to the critical velocity, and find that this relationship is in good agreement with the numerical simulations carried out on the nonlocal Gross-Pitaevskii equation.
Address [Mason, Peter] Univ Durham, Dept Phys, Durham DH1 3LE, England
Corporate Author Thesis
Publisher Amer Physical Soc Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0031-9007 ISBN Medium
Area Expedition Conference
Notes WOS:000306651900008 Approved
Call Number UAI @ eduardo.moreno @ Serial 229
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Author (up) Sepulveda, N.; Josserand, C.; Rica, S.
Title Superfluid density in a two-dimensional model of supersolid Type
Year 2010 Publication European Physical Journal B Abbreviated Journal Eur. Phys. J. B
Volume 78 Issue 4 Pages 439-447
Keywords
Abstract We study in 2-dimensions the superfluid density of periodically modulated states in the framework of the mean-field Gross-Pitaevskii model of a quantum solid. We obtain a full agreement for the superfluid fraction between a semi-theoretical approach and direct numerical simulations. As in 1-dimension, the superfluid density decreases exponentially with the amplitude of the particle interaction. We discuss the case when defects are present in this modulated structure. In the case of isolated defects (e.g. dislocations) the superfluid density only shows small changes. Finally, we report an increase of the superfluid fraction up to 50% in the case of extended macroscopical defects. We show also that this excess of superfluid fraction depends on the length of the complex network of grain boundaries in the system.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1434-6028 ISBN Medium
Area Expedition Conference
Notes WOS:000286669400004 Approved
Call Number UAI @ eduardo.moreno @ Serial 121
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