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

Rajarshi; Mohammad Saif Khan; Prateek Anand; Samriddhi Sankar Ray

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arXiv · 2512.10788

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

Rajarshi·Mohammad Saif Khan·Prateek Anand·Samriddhi Sankar Ray

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Abstract

The inviscid, partial differential equations of hydrodynamics when projected via a Galerkin-truncation on a finite-dimensional subspace spanning wavenumbers $-{\bf K}_{\rm G} \le {\bf k} \le {\bf K}_{\rm G}$, and hence retaining a finite number of modes $N_{\rm G}$, 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.

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physics.flu-dyn cond-mat.stat-mech nlin.CD

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Rajarshi, Mohammad Saif Khan, Prateek Anand, Samriddhi Sankar Ray. 2025-12-11. The dynamics of thermalisation in the Galerkin-truncated, three-dimensional Euler equation. https://arxiv.org/abs/2512.10788

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