The emergence of fast oscillations in a reduced primitive equation model and its implications for closure theories

Simple item page
dc.contributor.authorChekroun, Mickael D.en
dc.contributor.authorLiu, Honghuen
dc.contributor.authorMcWilliams, James C.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2019-10-04T14:40:50Zen
dc.date.available2019-10-04T14:40:50Zen
dc.date.issued2017-06-27en
dc.description.abstractThe problem of emergence of fast gravity-wave oscillations in rotating, stratified flow is reconsidered. Fast inertia-gravity oscillations have long been considered an impediment to initialization of weather forecasts, and the concept of a "slow manifold" evolution, with no fast oscillations, has been hypothesized. It is shown on a reduced Primitive Equation model introduced by Lorenz in 1980 that fast oscillations are absent over a finite interval in Rossby number but they can develop brutally once a critical Rossby number is crossed, in contradistinction with fast oscillations emerging according to an exponential smallness scenario such as reported in previous studies, including some others by Lorenz. The consequences of this dynamical transition on the closure problem based on slow variables is also discussed. In that respect, a novel variational perspective on the closure problem exploiting manifolds is introduced. This framework allows for a unification of previous concepts such as the slow manifold or other concepts of "fuzzy" manifold. It allows furthermore for a rigorous identification of an optimal limiting object for the averaging of fast oscillations, namely the optimal parameterizing manifold (PM). It is shown through detailed numerical computations and rigorous error estimates that the manifold underlying the nonlinear Balance Equations provides a very good approximation of this optimal PM even somewhat beyond the emergence of fast and energetic oscillations. (C) 2016 The Authors. Published by Elsevier Ltd.en
dc.description.notesThis work has been partially supported by the Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) grant N00014-12-1-0911 and N00014-16-1-2073 (MDC). We thank one of the anonymous reviewers. His/her inspiring and constructive remarks were greatly appreciated.en
dc.description.sponsorshipOffice of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) [N00014-12-1-0911, N00014-16-1-2073]en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1016/j.compfluid.2016.07.005en
dc.identifier.eissn1879-0747en
dc.identifier.issn0045-7930en
dc.identifier.urihttp://hdl.handle.net/10919/94350en
dc.identifier.volume151en
dc.language.isoenen
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectParameterizing manifoldsen
dc.subjectSlow manifoldsen
dc.subjectSlow conditional expectationsen
dc.subjectEmergence of fast oscillationsen
dc.subjectBalance equationsen
dc.titleThe emergence of fast oscillations in a reduced primitive equation model and its implications for closure theoriesen
dc.title.serialComputers & Fluidsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.dcmitypeStillImageen

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
1-s2.0-S004579301630216X-main.pdf
Size:
9.58 MB
Format:
Adobe Portable Document Format
Description:
Download

Collections

Scholarly Works, Mathematics