One-dimensional hydrodynamic model generating a turbulent cascade

Takeshi Matsumoto and Takashi Sakajo
Phys. Rev. E 93, 053101 – Published 2 May 2016

Abstract

As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analog (enstrophy) in the inviscid case. With a large-scale random forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency, and self-similarity in the dynamical system structure.

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  • Received 6 October 2015
  • Revised 22 February 2016

DOI:https://doi.org/10.1103/PhysRevE.93.053101

©2016 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Takeshi Matsumoto1,* and Takashi Sakajo2,†

  • 1Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan
  • 2Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan

  • *takeshi@kyoryu.scphys.kyoto-u.ac.jp
  • sakajo@math.kyoto-u.ac.jp

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Issue

Vol. 93, Iss. 5 — May 2016

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