Related Experiment Video
Updated: Jun 22, 2026

Evolution of Staircase Structures in Diffusive Convection
Published on: September 5, 2018
Cascades, thermalization, and eddy viscosity in helical Galerkin truncated Euler flows
G Krstulovic1, P D Mininni, M E Brachet
1Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, associé au CNRS et aux Universités Paris VI et VII, 24 Rue Lhomond, 75231 Paris, France.
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.
Related Concept Videos
Euler's Equations of Motion
Eulerian and Lagrangian Flow Descriptions
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
Couette Flow
Steady, Laminar Flow Between Parallel Plates
Navier–Stokes Equations
Bernoulli's Equation for Flow Along a Streamline
