{"paper":{"title":"On the Non-Markovian Navier-Stokes Framework for Turbulence Modeling -- A Preliminary Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Ehsan Ghaderi, Siamak Kazemzadeh Hannani","submitted_at":"2025-08-03T18:55:05Z","abstract_excerpt":"This study explores a formulation of the Navier Stokes equations (NSE) using fractional calculus in modeling turbulence. By generalizing the stress strain constitutive relation to incorporate nonlocal spatial interactions and memory effects, we redefine a fractional Navier Stokes equation (fNSE). Regarding the inertial range scaling, the fractional Laplacian of order 1/3 and time fractional derivative capture non Markovian energy transfer. The one dimensional advection diffusion equation, for the purpose of initial validation and Burgers non-linear equation for the energy spectrum behavior are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.01890","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.01890/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}