{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T15:30:48Z","timestamp":1781278248350,"version":"3.54.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"name":"NSF","award":["DMS 1216465"],"award-info":[{"award-number":["DMS 1216465"]}]},{"name":"NSF","award":["AFOSR FA9550-12-1-0191"],"award-info":[{"award-number":["AFOSR FA9550-12-1-0191"]}]},{"DOI":"10.13039\/501100004410","name":"TUBITAK","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This report develops an ensemble or statistical eddy viscosity model.\nThe model is parameterized by an ensemble of solutions of an ensemble-Leray\nregularization. The combined approach of ensemble time stepping and ensemble\neddy viscosity modeling allows direct parametrization of the turbulent\nviscosity coefficient. We prove unconditional stability and that the model's solution approaches statistical equilibrium as <jats:italic>t<\/jats:italic> \u2192 \u221e; the model's variance converges to zero as <jats:italic>t<\/jats:italic> \u2192 \u221e. The ensemble method is used to interrogate a rotating flow, testing its predictability by computing effective averaged Lyapunov exponents.<\/jats:p>","DOI":"10.1515\/cmam-2014-0029","type":"journal-article","created":{"date-parts":[[2014,12,23]],"date-time":"2014-12-23T17:04:35Z","timestamp":1419354275000},"page":"173-188","source":"Crossref","is-referenced-by-count":37,"title":["Analysis of Model Variance for Ensemble Based Turbulence Modeling"],"prefix":"10.1515","volume":"15","author":[{"given":"Nan","family":"Jiang","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Songul","family":"Kaya","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Middle East Technical University, Ankara 06800, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William","family":"Layton","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2014,12,23]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/15\/2\/article-p173.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0029\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0029\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T22:40:05Z","timestamp":1680302405000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0029\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,23]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,3,10]]},"published-print":{"date-parts":[[2015,4,1]]}},"alternative-id":["10.1515\/cmam-2014-0029"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2014-0029","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,23]]}}}