The dynamics of thermalisation in the Galerkin-truncated, three-dimensional Euler equation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909957127929856 |
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| author | Rajarshi Khan, Mohammad Saif Anand, Prateek Ray, Samriddhi Sankar |
| author_facet | Rajarshi Khan, Mohammad Saif Anand, Prateek Ray, Samriddhi Sankar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The dynamics of thermalisation in the Galerkin-truncated, three-dimensional Euler equation Rajarshi Khan, Mohammad Saif Anand, Prateek Ray, Samriddhi Sankar Fluid Dynamics Statistical Mechanics Chaotic Dynamics 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. |
| title | The dynamics of thermalisation in the Galerkin-truncated, three-dimensional Euler equation |
| topic | Fluid Dynamics Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2512.10788 |