{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T21:10:43Z","timestamp":1767474643961,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2012,1,4]],"date-time":"2012-01-04T00:00:00Z","timestamp":1325635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Statistical dynamical closures for inhomogeneous turbulence described by multi\u2011field equations are derived based on renormalized perturbation theory. Generalizations of the computationally tractable quasi-diagonal direct interaction approximation for inhomogeneous barotropic turbulent flows over topography are developed. Statistical closures are also formulated for large eddy simulations including subgrid models that ensure the same large scale statistical behavior as higher resolution closures. The focus is on baroclinic quasigeostrophic and three-dimensional inhomogeneous turbulence although the framework is generally applicable to classical field theories with quadratic nonlinearity.<\/jats:p>","DOI":"10.3390\/e14010032","type":"journal-article","created":{"date-parts":[[2012,1,4]],"date-time":"2012-01-04T17:44:06Z","timestamp":1325699046000},"page":"32-57","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Statistical Dynamical Closures and Subgrid Modeling for Inhomogeneous QG and 3D Turbulence"],"prefix":"10.3390","volume":"14","author":[{"given":"Jorgen S.","family":"Frederiksen","sequence":"first","affiliation":[{"name":"Centre for Australian Weather and Climate Research, CSIRO Marine and Atmospheric Research, PMB#1, Aspendale, Victoria, 3195, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2012,1,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"635","DOI":"10.3390\/e10040635","article-title":"Entropy, closures and subgrid modeling","volume":"10","author":"Frederiksen","year":"2008","journal-title":"Entropy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3006","DOI":"10.1175\/JAS3795.1","article-title":"Dynamical subgrid-scale parameterizations from direct numerical simulations","volume":"63","author":"Frederiksen","year":"2006","journal-title":"J. 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