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

Abstract

The inviscid, partial differential equations of hydrodynamics when projected via a Galerkin-truncation on a finite-dimensional subspace spanning wavenumbers $-{\mathbf{K}}_{\mathrm{G}}\le \mathbf{k}\le {\mathbf{K}}_{\mathrm{G}}$, and hence retaining a finite number of modes $N_{\mathrm{G}}$, lead to absolute equilibrium states. We review how the Galerkin-truncated, three-dimensional, incompressible Euler equation thermalises 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 thermalisation.

A mini review and new results. 9 pages and 3 figures. Comments are welcome