Entropy budget and coherent structures associated with a spectral closure model of turbulence

TitleEntropy budget and coherent structures associated with a spectral closure model of turbulence
Publication TypeJournal Article
Year of Publication2018
AuthorsSalmon R
JournalJournal of Fluid Mechanics
Volume857
Pagination806-822
Date Published2018/10
Type of ArticleArticle
ISBN Number0022-1120
Accession NumberWOS:000448524100001
Keywords2-dimensional turbulence; approximation; dynamics; homogeneous turbulence; mechanics; physics; turbulence theory; turbulent flows
Abstract

We 'derive' the eddy-damped quasi-normal Markovian model (EDQNM) by a method that replaces the exact equation for the Fourier phases with a solvable stochastic model, and we analyse the entropy budget of the EDQNM. We show that a quantity that appears in the probability distribution of the phases may be interpreted as the rate at which entropy is transferred from the Fourier phases to the Fourier amplitudes. In this interpretation, the decrease in phase entropy is associated with the formation of structures in the flow, and the increase of amplitude entropy is associated with the spreading of the energy spectrum in wavenumber space. We use Monte Carlo methods to sample the probability distribution of the phases predicted by our theory. This distribution contains a single adjustable parameter that corresponds to the triad correlation time in the EDQNM. Flow structures form as the triad correlation time becomes very large, but the structures take the form of vorticity quadrupoles that do not resemble the monopoles and dipoles that are actually observed.

DOI10.1017/jfm.2018.778
Short TitleJ. Fluid Mech.
Student Publication: 
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