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

Published online by Cambridge University Press:  29 October 2018

Rick Salmon Open the ORCID record for Rick Salmon [Opens in a new window]
Rick Salmon*
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093-0213, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , pp. 806 - 822
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Copyright
© 2018 Cambridge University Press 

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