Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows

AMS Citation:
Krstulovic, G., P. D. Mininni, M. E. Brachet, and A. Pouquet, 2009: Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows. Physical Review E, 79, 056304, doi:10.1103/PhysRevE.79.056304.
Date:2009-05-06
Resource Type:article
Title:Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows
Abstract: The dynamics of the truncated Euler equations with helical initial conditions are studied. Transient energy and helicity cascades leading to Kraichnan helical absolute equilibrium at small scales, including a linear scaling of the relative helicity spectrum are obtained. Strong helicity effects are found using initial data concentrated at high wave numbers. Using low-wave-number initial conditions, the results of Cichowlas et al. [Phys. Rev. Lett. 95, 264502 (2005)] are extended to helical flows. Similarities between the turbulent transient evolution of the ideal (time-reversible) system and viscous helical flows are found. Using an argument in the manner of Frisch et al. [Phys. Rev. Lett. 101, 144501 (2008)], the excess of relative helicity found at small scales in the viscous run is related to the thermalization of the ideal flow. The observed differences in the behavior of truncated Euler and (constant viscosity) Navier-Stokes are qualitatively understood using the concept of eddy viscosity. The large scales of truncated Euler equations are then shown to follow quantitatively an effective Navier-Stokes dynamics based on a variable (scale dependent) eddy viscosity.
Peer Review:Refereed
Copyright Information:Copyright 2009 American Physical Society
OpenSky citable URL: ark:/85065/d7rn38wm
Publisher's Version: 10.1103/PhysRevE.79.056304
Author(s):
  • G. Krstulovic
  • Pablo Mininni - NCAR/UCAR
  • Marc Brachet - NCAR/UCAR
  • Annick Pouquet - NCAR/UCAR
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