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

TL;DR

This paper investigates the behavior of helical truncated Euler flows, revealing transient cascades, thermalization, and an effective eddy viscosity that links ideal Euler dynamics with viscous flows, extending previous findings to helical cases.

Contribution

It demonstrates for the first time the transient cascades and thermalization in helical truncated Euler flows and establishes a quantitative link to viscous flows via scale-dependent eddy viscosity.

Findings

Transient energy and helicity cascades observed.

Truncated Euler flows exhibit thermalization at small scales.

Large-scale dynamics follow an effective Navier-Stokes model with variable eddy viscosity.

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 are obtained for the first time. 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. 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.