The dynamics of thermalization in the Galerkin-truncated, three-dimensional Euler equation

The three-dimensional (3D) incompressible Euler equation when projected via a Galerkin truncation on a finite-dimensional subspace spanning wavenumbers -KG≤k≤KG, and hence retaining a finite number of modes NG, leads to absolute equilibrium states. We review how this system thermalizes and its connection to questions in turbulence. We also discuss an emergent pseudo-dissipation range in the energy spectrum and the time scales associated with thermalization. This article is part of the theme issue ‘Frontiers of turbulence and statistical physics’.