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The role of coherent structures and inhomogeneity in near-field interscale turbulent energy transfers

Published online by Cambridge University Press:  01 June 2020

F. Alves Portela Open the ORCID record for F. Alves Portela [Opens in a new window] ,
G. Papadakis Open the ORCID record for G. Papadakis [Opens in a new window]  and
J. C. Vassilicos Open the ORCID record for J. C. Vassilicos [Opens in a new window]
F. Alves Portela*
Affiliation:
School of Engineering Sciences, University of Southampton, SouthamptonSO17 1BJ, UK
G. Papadakis
Affiliation:
Department of Aeronautics, Imperial College London, LondonSW7 2AZ, UK
J. C. Vassilicos*
Affiliation:
University of Lille, CNRS, ONERA, Arts et Métiers ParisTech, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des fluides de Lille – Kampé de Feriet, F-59000Lille, France
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We use direct numerical simulation data to study interscale and interspace energy exchanges in the near field of a turbulent wake of a square prism in terms of a Kármán–Howarth–Monin–Hill (KHMH) equation written for a triple decomposition of the velocity field which takes into account the presence of quasi-periodic vortex shedding coherent structures. Concentrating attention on the plane of the mean flow and on the geometric centreline, we calculate orientation averages of every term in the KHMH equation. The near field considered here ranges between two and eight times the width $d$ of the square prism and is very inhomogeneous and out of equilibrium so that non-stationarity and inhomogeneity contributions to the KHMH balance are dominant. The mean flow produces kinetic energy which feeds the vortex shedding coherent structures. In turn, these coherent structures transfer their energy to the stochastic turbulent fluctuations over all length scales $r$ from the Taylor length $\unicode[STIX]{x1D706}$ to $d$ and dominate spatial turbulent transport of small-scale two-point stochastic turbulent fluctuations. The orientation-averaged nonlinear interscale transfer rate $\unicode[STIX]{x1D6F1}^{a}$ which was found to be approximately independent of $r$ by Alves Portela et al. (J. Fluid Mech., vol. 825, 2017, pp. 315–352) in the range $\unicode[STIX]{x1D706}\leqslant r\leqslant 0.3d$ at a distance $x_{1}=2d$ from the square prism requires an interscale transfer contribution of coherent structures for this approximate constancy. However, the near constancy of $\unicode[STIX]{x1D6F1}^{a}$ in the range $\unicode[STIX]{x1D706}\leqslant r\leqslant d$ at $x_{1}=8d$ which was also found by Alves Portela et al. (2017) is mostly attributable to stochastic fluctuations. Even so, the proximity of $-\unicode[STIX]{x1D6F1}^{a}$ to the turbulence dissipation rate $\unicode[STIX]{x1D700}$ in the range $\unicode[STIX]{x1D706}\leqslant r\leqslant d$ at $x_{1}=8d$ does require interscale transfer contributions of the coherent structures. Spatial inhomogeneity also makes a direct and distinct contribution to $\unicode[STIX]{x1D6F1}^{a}$, and the constancy of $-\unicode[STIX]{x1D6F1}^{a}/\unicode[STIX]{x1D700}$ close to $1$ would not have been possible without it either in this near-field flow. Finally, the pressure-velocity term is also an important contributor to the KHMH balance in this near field, particularly at scales $r$ larger than approximately $0.4d$, and appears to correlate with the purely stochastic nonlinear interscale transfer rate when the orientation average is lifted.

JFM classification

Turbulent Flows: Turbulence theory Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 896 , 10 August 2020 , A16
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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