Invariants of the velocity gradient tensor in a spatially developing inhomogeneous turbulent flow

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Title: Invariants of the velocity gradient tensor in a spatially developing inhomogeneous turbulent flow
Author(s): Buxton, O
Breda, M
Chen, X
Item Type: Journal Article
Abstract: Tomographic PIV experiments were performed in the near-fiel d of the turbulent flow past a square cylinder. A classical Reynolds decomposition was p erformed on the resulting velocity fields into a time invariant mean flow and a fluctuatin g velocity field. This fluc- tuating velocity field was then further decomposed into cohe rent and residual/stochastic fluctuations. The statistical distributions of the second a nd third invariants of the ve- locity gradient tensor were then computed at various stream wise locations, along the centre line of the flow and within the shear layers. These inva riants were calculated from both the Reynolds-decomposed fluctuating velocity fields an d the coherent and stochas- tic fluctuating velocity fields. The range of spatial locatio ns probed incorporates regions of contrasting flow physics, including a mean recirculation region and separated shear layers, both upstream and downstream of the location of peak turbulence intensity along the centre line. These different flow physics are also reflecte d in the velocity gradients themselves with different topologies, as characterised by t he statistical distributions of the constituent enstrophy and strain-rate invariants, for the three different fluctuating velocity fields. Despite these differing flow physics the ubiq uitous self-similar “tear drop”- shaped joint probability density function between the seco nd and third invariants of the velocity gradient tensor is observed along the centre line a nd shear layer when calcu- lated from both the Reynolds decomposed and the stochastic v elocity fluctuations. These “tear drop”-shaped joint probability density functions ar e not, however, observed when calculated from the coherent velocity fluctuations. This “t ear drop” shape is classically associated to the statistical distribution of the velocity gradient tensor invariants in fully developed turbulent flows in which there are no coherent dyna mics present, and hence spectral peaks at low wavenumbers. The results presented in this manuscript, however, show that such “tear drops” also exist in spatially developi ng inhomogeneous turbulent flows. This suggests that the “tear drop” shape may not just be a universal feature of fully developed turbulence but of turbulent flows in general.
Publication Date: 15-Mar-2017
Date of Acceptance: 6-Feb-2017
ISSN: 1469-7645
Publisher: Cambridge University Press (CUP)
Start Page: 1
End Page: 20
Journal / Book Title: Journal of Fluid Mechanics
Volume: 817
Copyright Statement: © Cambridge University Press 2017. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/L023520/1
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
shear layer turbulence
turbulent flows
vortex streets
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Faculty of Engineering

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