{"id":5538,"date":"2026-01-01T05:00:00","date_gmt":"2026-01-01T10:00:00","guid":{"rendered":"http:\/\/mseas.mit.edu\/?p=5538"},"modified":"2026-02-02T10:41:23","modified_gmt":"2026-02-02T15:41:23","slug":"rigid-sets-and-coherent-sets-in-realistic-ocean-flows","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=5538","title":{"rendered":"Rigid Sets and Coherent Sets in Realistic Ocean Flows"},"content":{"rendered":"\n<p>This paper focuses on the extractions of Lagrangian Coherent Sets from realistic velocity fields obtained from ocean data and simulations, each of which can be highly resolved and non volume-preserving. We introduce two novel methods for computing two formulations of such sets. First, we propose a new &#8220;diffeomorphism-based&#8221; criterion to extract &#8220;rigid sets&#8221;, defined as sets over which the flow map acts approximately as a rigid transformation. Second, we develop a matrix-free methodology that provides a simple and efficient framework to compute &#8220;coherent sets&#8221; with operator methods. Both new methods and their resulting <em>rigid sets<\/em> and <em>coherent sets<\/em> are illustrated and compared using three numerically simulated flow examples, including a high-resolution realistic, submesoscale to large-scale dynamic ocean current field in the Palau Island region of the western Pacific Ocean.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This paper focuses on the extractions of Lagrangian Coherent Sets from realistic velocity fields obtained from ocean data and simulations, each of which can be highly resolved and non volume-preserving. We introduce two novel methods for computing two formulations of such sets. First, we propose a new &#8220;diffeomorphism-based&#8221; criterion to extract &#8220;rigid sets&#8221;, defined as [&hellip;]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[32,28,5,189,54,190],"tags":[220,221,207,218],"class_list":["post-5538","post","type-post","status-publish","format-standard","hentry","category-numerical-ocean-modeling","category-multiscale-ocean-modeling","category-publications","category-lagrangian-modeling","category-papers-in-refereed-journals-multiscale-ocean-modeling","category-papers-in-refereed-journals-lagrangian-modeling","tag-bayesian-data-assimilation","tag-fleat","tag-in-bda","tag-nsf-alpha"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/5538","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\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5538"}],"version-history":[{"count":2,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/5538\/revisions"}],"predecessor-version":[{"id":5971,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/5538\/revisions\/5971"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5538"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5538"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}