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On velocity gradient dynamics and turbulent structure

Published online by Cambridge University Press:  02 September 2015

J. M. Lawson  and
J. R. Dawson
J. M. Lawson*
Affiliation:
Engineering Department, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
J. R. Dawson
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
*
†Email address for correspondence: [email protected]
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Abstract

The statistics of the velocity gradient tensor $\unicode[STIX]{x1D63C}=\boldsymbol{{\rm\nabla}}\boldsymbol{u}$, 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 $\unicode[STIX]{x1D63C}$. Structures are studied through the footprints they leave in conditional averages of the $Q=-\text{Tr}(\unicode[STIX]{x1D63C}^{2})/2$ field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the $Q$ field conditioned upon $\unicode[STIX]{x1D63C}$ 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.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 780 , 10 October 2015 , pp. 60 - 98
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Copyright
© 2015 Cambridge University Press 

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