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'.
Authors
- Prateek Anand (ORCID: https://orcid.org/0000-0001-6922-0894)
- Samriddhi Sankar Ray (ORCID: https://orcid.org/0000-0001-9407-0007)
- C Rajarshi (ORCID: https://orcid.org/0009-0009-1747-3916)
- Mohammad Saif Khan
Institutions
- Indian Institute of Technology Bombay (IN)
- International Centre for Theoretical Sciences (IN)
Publication Details
- Journal
- Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
- Published
- 2026-07-30
- DOI
- https://doi.org/10.1098/rsta.2025.0024
- Primary Topic
- Navier-Stokes equation solutions
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Department of Atomic Energy, Government of India
- Indo-French Centre for the Promotion of Advanced Research