{"id":2289,"date":"2013-08-09T10:01:23","date_gmt":"2013-08-09T14:01:23","guid":{"rendered":"http:\/\/mseas.mit.edu\/?p=2289"},"modified":"2021-07-06T13:16:58","modified_gmt":"2021-07-06T17:16:58","slug":"global-analysis-of-navier-stokes-and-boussinesq-stochastic-flows-using-dynamical-orthogonality","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=2289","title":{"rendered":"Global Analysis of Navier-Stokes and Boussinesq Stochastic Flows using Dynamical Orthogonality"},"content":{"rendered":"We provide a new framework for the study of fl\u0087uid \u0087flows presenting complex uncertain\r\nbehavior. Our approach is based on the stochastic reduction and analysis of the governing\r\nequations using the dynamically orthogonal field equations. By numerically solving these\r\nequations we evolve in a fully coupled way the mean fl\u0087ow and the statistical and spatial\r\ncharacteristics of the stochastic fl\u0087uctuations. This set of equations is formulated for\r\nthe general case of stochastic boundary conditions and allows for the application of\r\nprojection methods that reduce considerably the computational cost. We analyze the\r\ntransformation of energy from stochastic modes to mean dynamics, and vice-versa, by\r\nderiving exact expressions that quantify the interaction among different components\r\nof the fl\u0087ow. The developed framework is illustrated through specifi\u0085c fl\u0087ows in unstable\r\nregimes. In particular, we consider the \u0087flow behind a disk and the Rayleigh\u0096-B\u00e9nard\r\nconvection, for which we construct bifurcation diagrams that describe the variation of\r\nthe response as well as the energy transfers for different parameters associated with\r\nthe considered \u0087flows. We reveal the low-dimensionality of the underlying stochastic\r\nattractor.","protected":false},"excerpt":{"rendered":"<p>We provide a new framework for the study of fl\u0087uid \u0087flows presenting complex uncertain behavior. Our approach is based on the stochastic reduction and analysis of the governing equations using the dynamically orthogonal field equations. By numerically solving these equations we evolve in a fully coupled way the mean fl\u0087ow and the statistical and spatial [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31,37,33,38,9,5,59,64],"tags":[],"class_list":["post-2289","post","type-post","status-publish","format-standard","hentry","category-uncertainty-quantification-and-reduced-order-modeling","category-applications-to-ocean-dynamics","category-uncertainty-quantification-and-predictions","category-physical-oceanography","category-papers-submitted","category-publications","category-papers-in-refereed-journals-physical-oceanography","category-papers-in-refereed-journals-uncertainty-quantification-and-predictions"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/2289","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2289"}],"version-history":[{"count":11,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/2289\/revisions"}],"predecessor-version":[{"id":2980,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/2289\/revisions\/2980"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2289"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2289"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}