{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T09:01:14Z","timestamp":1718701274718},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,20]],"date-time":"2018-07-20T00:00:00Z","timestamp":1532044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"In two recent papers we introduced a generalization of Boltzmann\u2019s assumption of molecular chaos based on a criterion of maximum entropy, which allowed setting up a bilocal version of Boltzmann\u2019s kinetic equation. The present paper aims to investigate how the essentially non-local character of turbulent flows can be addressed through this bilocal kinetic description, instead of the more standard approach through the local Euler\/Navier\u2013Stokes equation. Balance equations appropriate to this kinetic scheme are derived and closed so as to provide bilocal hydrodynamical equations at the non-viscous order. These equations essentially consist of two copies of the usual local equations, but coupled through a bilocal pressure tensor. Interestingly, our formalism automatically produces a closed transport equation for this coupling term.<\/jats:p>","DOI":"10.3390\/e20070539","type":"journal-article","created":{"date-parts":[[2018,7,23]],"date-time":"2018-07-23T07:24:27Z","timestamp":1532330667000},"page":"539","source":"Crossref","is-referenced-by-count":1,"title":["Turbulence through the Spyglass of Bilocal Kinetics"],"prefix":"10.3390","volume":"20","author":[{"given":"Gregor","family":"Chliamovitch","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, Switzerland"}]},{"given":"Yann","family":"Thorimbert","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, Switzerland"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,20]]},"reference":[{"key":"ref_1","unstructured":"Batchelor, G.K. (1953). The Theory of Homogeneous Turbulence, Cambridge University Press."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Davidson, P.A. (2015). Turbulence: An Introduction for Scientists and Engineers, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780198722588.001.0001"},{"key":"ref_3","first-page":"192","article-title":"On the Statistical Theory of Isotropic Turbulence","volume":"164","author":"Howarth","year":"1938","journal-title":"Proc. R. Soc. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02780991","article-title":"Statistical hydrodynamics","volume":"6","author":"Onsager","year":"1949","journal-title":"Nuovo Cimento Suppl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1103\/RevModPhys.78.87","article-title":"Onsager and the theory of hydrodynamic turbulence","volume":"78","author":"Eyink","year":"2006","journal-title":"Rev. Mod. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1017\/S0022112059000362","article-title":"Structure of isotropic turbulence at very high Reynolds numbers","volume":"5","author":"Kraichnan","year":"1959","journal-title":"J. Fluid Mech."},{"key":"ref_7","unstructured":"Kreuzer, H.J. (1981). Nonequilibrium Thermodynamics and Its Statistical Foundations, Oxford University Press."},{"key":"ref_8","unstructured":"Liboff, R.L. (2003). Kinetic Theory, Springer."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7522","DOI":"10.3390\/e17117522","article-title":"A Truncation Scheme for the BBGKY2 Equation","volume":"17","author":"Chliamovitch","year":"2015","journal-title":"Entropy"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Chliamovitch, G., Malaspinas, O., and Chopard, B. (2017). Kinetic Theory beyond the Stosszahlansatz. 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(2006). Modelling and Numerics of Kinetic Dissipative Systems, Nova Science Publishers."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/7\/539\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T19:57:24Z","timestamp":1718135844000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/7\/539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,20]]},"references-count":19,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2018,7]]}},"alternative-id":["e20070539"],"URL":"https:\/\/doi.org\/10.3390\/e20070539","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,20]]}}}