{"paper":{"title":"A theory of hydrodynamic turbulence based on non-equilibrium statistical mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"David Ruelle","submitted_at":"2017-07-09T12:03:46Z","abstract_excerpt":"In earlier papers we have studied the turbulent flow exponents $\\zeta_p$, where $\\langle|\\Delta{\\bf v}|^p\\rangle\\sim\\ell^{\\zeta_p}$ is the contribution to the fluid velocity at small scale $\\ell$. Using ideas of non-equilibrium statistical mechanics we have found $$ \\zeta_p={p\\over3}-{1\\over\\ln\\kappa}\\ln\\Gamma({p\\over3}+1) $$ where $1/ln\\kappa$ is experimentally $\\approx 0.32\\pm 0.01$. The purpose of the present note is to propose a somewhat more physical derivation of the formula for $\\zeta_p$. We also present an estimate $\\approx 100$ for the Reynolds number at the onset of turbulence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02567","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}