{"paper":{"title":"On URANS Congruity with Time Averaging: Analytical laws suggest improved models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Michael McLaughlin, William Layton","submitted_at":"2019-07-23T18:30:39Z","abstract_excerpt":"The standard $1-$equation model \\ of turbulence was first derived by Prandtl and has evolved to be a common method for practical flow simulations. Five fundamental laws that any URANS model should satisfy are \\[ \\begin{array} [c]{ccc} \\textbf{1.} & \\text{Time window:} & \\begin{array} [c]{c} \\tau\\downarrow 0\\text{ implies }v_{\\text{{\\small URANS}}}\\rightarrow u_{\\text{{\\small NSE}}}\\text{ \\&}\\\\ \\text{ }\\tau\\uparrow\\text{implies }\\nu_{T}\\uparrow \\end{array} \\\\ \\textbf{2.} & l(x)=0\\ \\text{at walls:} & l(x)\\rightarrow 0\\text{ as }x\\rightarrow walls,\\\\ \\textbf{3.} & \\text{ Bounded energy:} & \\sup_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10092","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"}