{"paper":{"title":"Turbulence Modeling via the Fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Benoit Cushman-Roisin, Brenden P. Epps","submitted_at":"2018-03-14T14:01:37Z","abstract_excerpt":"Herein, we derive the fractional Laplacian operator as a means to represent the mean friction force arising in a turbulent flow: $ \\rho \\frac{D\\bar{\\bf u}}{Dt} = -\\nabla p + \\mu_\\alpha \\nabla^2\\bar{\\bf u} + \\rho C_\\alpha \\iiint_{\\!-\\infty}^\\infty\n  \\frac{ \\bar{\\bf u}{\\scriptstyle(t,{\\bf x}')} - \\bar{\\bf u}{\\scriptstyle(t,{\\bf x})} }{|{\\bf x}'-{\\bf x}|^{\\alpha+3}} \\,d{\\bf x}' $, where $\\bar{\\bf u}{\\scriptstyle(t,{\\bf x})}$ is the ensemble-averaged velocity field, $\\mu_\\alpha$ is an enhanced molecular viscosity, and $C_\\alpha$ is a turbulent mixing coefficient (with units (length)$^\\alpha$/(time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05286","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"}