Response maxima in modulated turbulence. II. Numerical simulations

Anna von der Heydt, Siegfried Grossmann, and Detlef Lohse
Phys. Rev. E 68, 066302 – Published 15 December 2003
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Abstract

Numerical simulations of fully developed turbulence driven by a modulated energy input rate or driving force are performed within two dynamical cascade models, the Gkedzer-Ohkitani-Yamada shell model and a reduced wave vector set approximation of the Navier-Stokes equation. The frequency behavior of the system response is studied and compared with predictions from a variable range mean-field theory, which excludes turbulent fluctuations. In agreement with the mean-field approach, we find a constant response amplitude for low driving frequencies and a 1/ω decay of the amplitude for high frequencies. In the mean-field theory, the finite cascade time scale had led to an oscillating behavior of the response amplitude as a function of the driving frequency. In the simulations of both models we observe the main maximum. The higher maxima and minima are completely washed out by fluctuations, though the statistical properties of the fluctuations are different in the two models.

  • Received 13 February 2003

DOI:https://doi.org/10.1103/PhysRevE.68.066302

©2003 American Physical Society

Authors & Affiliations

Anna von der Heydt1,2,*, Siegfried Grossmann1, and Detlef Lohse2

  • 1Fachbereich Physik, Philipps-Universität Marburg, Renthof 6, 35032 Marburg, Germany
  • 2Department of Applied Physics and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands

  • *Present address: Department of Physics and Astronomy, Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.

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Vol. 68, Iss. 6 — December 2003

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