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The turbulence cascade in the near wake of a square prism

Published online by Cambridge University Press:  20 July 2017

F. Alves Portela Open the ORCID record for F. Alves Portela [Opens in a new window] ,
G. Papadakis  and
J. C. Vassilicos Open the ORCID record for J. C. Vassilicos [Opens in a new window]
F. Alves Portela*
Affiliation:
Turbulence, Mixing and Flow Control Group, Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
G. Papadakis
Affiliation:
Turbulence, Mixing and Flow Control Group, Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
J. C. Vassilicos*
Affiliation:
Turbulence, Mixing and Flow Control Group, Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We present a study of the turbulence cascade on the centreline of an inhomogeneous and anisotropic near-field turbulent wake generated by a square prism at a Reynolds number of $Re=3900$ using the Kármán–Howarth–Monin–Hill equation. This is the fully generalised scale-by-scale energy balance which, unlike the Kármán–Howarth equation, does not require homogeneity or isotropy assumptions. Our data are obtained from a direct numerical simulation and therefore enable us to access all of the processes involved in this energy balance. A significant range of length scales exists where the orientation-averaged nonlinear interscale transfer rate is approximately constant and negative, indicating a forward turbulence cascade on average. This average cascade consists of coexisting forward and inverse cascade behaviours in different scale-space orientations. With increasing distance from the prism but within the near field of the wake, the orientation-averaged nonlinear interscale transfer rate tends to be approximately equal to minus the turbulence dissipation rate even though all of the inhomogeneity-related energy processes in the scale-by-scale energy balance are significant, if not equally important. We also find well-defined near $-5/3$ energy spectra in the streamwise direction, in particular at a centreline position where the inverse cascade behaviour occurs for streamwise oriented length scales.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 315 - 352
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© 2017 Cambridge University Press 

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