Strong turbulence for vibrating plates: Emergence of a Kolmogorov spectrum

Gustavo Düring, Christophe Josserand, Giorgio Krstulovic, and Sergio Rica
Phys. Rev. Fluids 4, 064804 – Published 13 June 2019
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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.

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  • Received 29 October 2018

DOI:https://doi.org/10.1103/PhysRevFluids.4.064804

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Gustavo Düring1, Christophe Josserand2, Giorgio Krstulovic3, and Sergio Rica2,4,*

  • 1Instituto de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile
  • 2LadHyX, CNRS and Ecole Polytechnique, UMR 7646, IP Paris, 91128 Palaiseau, France
  • 3Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire, CS 34229, 06304 Nice cedex 4, France
  • 4Facultad de Ingeniería y Ciencias and UAI Physics Center, Universidad Adolfo Ibáñez, Avenida Diagonal las Torres 2640, Peñalolén, Santiago, Chile

  • *sergio.rica@uai.cl

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Issue

Vol. 4, Iss. 6 — June 2019

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