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The dynamics of the truncated Euler equations with helical initial conditionsare studied. Transient energy and helicity cascades leading to Kraichnanhelical absolute equilibrium at small scales are obtained for the first time.The results of [Cichowlas et al. Phys. Rev. Lett. 95, 264502 (2005)] areextended to helical flows. Similarities between the turbulent transientevolution of the ideal (time-reversible) system and viscous helical flows arefound. The observed differences in the behavior of truncated Euler and(constant viscosity) Navier-Stokes are qualitatively understood using theconcept of eddy viscosity. The large scales of truncated Euler equations arethen shown to follow quantitatively an effective Navier-Stokes dynamics basedon a variable (scale dependent) eddy viscosity.

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