On velocity gradient dynamics and turbulent structure
On velocity gradient dynamics and turbulent structure
The statistics of the velocity gradient tensor A = ∇∇u, which embody the fine scales of turbulence, are influenced by turbulent ‘structure’. Whilst velocity gradient statistics and dynamics have been well characterised, the connection between structure and dynamics has largely focused on rotation-dominated flow and relied upon data from numerical simulation alone. Using numerical and spatially resolved experimental datasets of homogeneous turbulence, the role of structure is examined for all local (incompressible) flow topologies characterisable by A. Structures are studied through the footprints they leave in conditional averages of the Q = −Tr(A2)/2 field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the Q field conditioned upon A and educes quantitatively similar structure in both datasets, dissimilar to that of random Gaussian velocity fields. Moreover, it strongly resembles a promising model for velocity gradient dynamics recently proposed by Wilczek & Meneveau (J. Fluid Mech., vol. 756, 2014, pp. 191–225), but is derived under a less restrictive premise, with explicitly determined closure coefficients. The second technique examines true conditional averages of the Q field, which is used to validate the stochastic estimation and provide insights towards the model’s refinement. Jointly, these approaches confirm that vortex tubes are the predominant feature of rotation-dominated regions and additionally show that shear layer structures are active in strain-dominated regions. In both cases, kinematic features of these structures explain alignment statistics of the pressure Hessian eigenvectors and why local and non-local strain production act in opposition to each other.
60-98
Lawson, J.M.
4e0b1895-51c5-41e6-9322-7f79e76e0e4c
Dawson, J.R.
a0a9f5ed-0adc-4c02-aa71-0fb0caedcd14
10 October 2015
Lawson, J.M.
4e0b1895-51c5-41e6-9322-7f79e76e0e4c
Dawson, J.R.
a0a9f5ed-0adc-4c02-aa71-0fb0caedcd14
Lawson, J.M. and Dawson, J.R.
(2015)
On velocity gradient dynamics and turbulent structure.
Journal of Fluid Mechanics, 780, .
(doi:10.1017/jfm.2015.452).
Abstract
The statistics of the velocity gradient tensor A = ∇∇u, which embody the fine scales of turbulence, are influenced by turbulent ‘structure’. Whilst velocity gradient statistics and dynamics have been well characterised, the connection between structure and dynamics has largely focused on rotation-dominated flow and relied upon data from numerical simulation alone. Using numerical and spatially resolved experimental datasets of homogeneous turbulence, the role of structure is examined for all local (incompressible) flow topologies characterisable by A. Structures are studied through the footprints they leave in conditional averages of the Q = −Tr(A2)/2 field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the Q field conditioned upon A and educes quantitatively similar structure in both datasets, dissimilar to that of random Gaussian velocity fields. Moreover, it strongly resembles a promising model for velocity gradient dynamics recently proposed by Wilczek & Meneveau (J. Fluid Mech., vol. 756, 2014, pp. 191–225), but is derived under a less restrictive premise, with explicitly determined closure coefficients. The second technique examines true conditional averages of the Q field, which is used to validate the stochastic estimation and provide insights towards the model’s refinement. Jointly, these approaches confirm that vortex tubes are the predominant feature of rotation-dominated regions and additionally show that shear layer structures are active in strain-dominated regions. In both cases, kinematic features of these structures explain alignment statistics of the pressure Hessian eigenvectors and why local and non-local strain production act in opposition to each other.
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Accepted/In Press date: 2 September 2015
e-pub ahead of print date: 2 September 2015
Published date: 10 October 2015
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Local EPrints ID: 435974
URI: http://eprints.soton.ac.uk/id/eprint/435974
ISSN: 0022-1120
PURE UUID: a27adcd1-52d3-486c-9899-baab6a310ab2
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Date deposited: 25 Nov 2019 17:30
Last modified: 17 Mar 2024 03:53
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J.R. Dawson
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