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Spatio-temporal fluctuations of interscale and interspace energy transfer dynamics in homogeneous turbulence

Published online by Cambridge University Press:  15 August 2023

H.S. Larssen Open the ORCID record for H.S. Larssen [Opens in a new window]  and
J.C. Vassilicos Open the ORCID record for J.C. Vassilicos [Opens in a new window]
H.S. Larssen*
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
J.C. Vassilicos*
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK UMR 9014 - LMFL - Laboratoire de Mécanique des fluides de Lille - Kampé de Feriet, Univ. Lille, CNRS, ONERA, Arts et Métiers ParisTech, Centrale Lille, F-59000 Lille, France
*
†Email addresses for correspondence: h.larssen18@imperial.ac.uk, john-christos.vassilicos@cnrs.fr
†Email addresses for correspondence: h.larssen18@imperial.ac.uk, john-christos.vassilicos@cnrs.fr
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Abstract

We study fluctuations of all co-existing energy exchange/transfer/transport processes in stationary periodic turbulence including those that average to zero and are not present in average cascade theories. We use a Helmholtz decomposition of accelerations that leads to a decomposition of all terms in the Kármán–Howarth–Monin–Hill (KHMH) equation (scale-by-scale two-point energy balance) causing it to break into two energy balances, one resulting from the integrated two-point vorticity equation and the other from the integrated two-point pressure equation. The various two-point acceleration terms in the Navier–Stokes difference (NSD) equation for the dynamics of two-point velocity differences have similar alignment tendencies with the two-point velocity difference, implying similar characteristics for the NSD and KHMH equations. We introduce the two-point sweeping concept and show how it articulates with the fluctuating interscale energy transfer as the solenoidal part of the interscale transfer rate does not fluctuate with turbulence dissipation at any scale above the Taylor length but with the sum of the time derivative and the solenoidal interspace transport rate terms. The pressure fluctuations play an important role in the interscale and interspace turbulence transfer/transport dynamics as the irrotational part of the interscale transfer rate is equal to the irrotational part of the interspace transfer rate and is balanced by two-point fluctuating pressure work. We also study the homogeneous/inhomogeneous decomposition of interscale transfer. The statistics of the latter are skewed towards forward cascade events whereas the statistics of the former are not. We also report statistics conditioned on intense forward/backward interscale transfer events.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Intermittency
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 969 , 25 August 2023 , A14
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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