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Symmetry transformation and dimensionality reduction of the anisotropic pressure Hessian

Published online by Cambridge University Press:  13 August 2020

M. Carbone Open the ORCID record for M. Carbone [Opens in a new window] ,
M. Iovieno Open the ORCID record for M. Iovieno [Opens in a new window]  and
A. D. Bragg Open the ORCID record for A. D. Bragg [Opens in a new window]
M. Carbone
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129Torino, Italy Department of Civil and Environmental Engineering, Duke University, Durham, NC27708, USA
M. Iovieno
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129Torino, Italy
A. D. Bragg*
Affiliation:
Department of Civil and Environmental Engineering, Duke University, Durham, NC27708, USA
*
†Email address for correspondence: andrew.bragg@duke.edu
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Abstract

The dynamics of the velocity gradient tensor in turbulence is governed in part by the anisotropic pressure Hessian, which is a non-local functional of the velocity gradient field. This anisotropic pressure Hessian plays a key dynamical role, for example in preventing finite-time singularities, but it is difficult to understand and model due to its non-locality and complexity. In this work a symmetry transformation for the pressure Hessian is introduced, such that when the transformation is applied to the original pressure Hessian, the dynamics of the invariants of the velocity gradients remains unchanged. We then exploit this symmetry transformation to perform a dimensional reduction on the three-dimensional anisotropic pressure Hessian, which, remarkably, is possible everywhere in the flow except on zero-measure sets. The dynamical activity of the newly introduced dimensionally reduced anisotropic pressure Hessian is confined to two-dimensional manifolds in the three-dimensional flow, and exhibits striking alignment properties with respect to the strain-rate eigenframe and the vorticity vector. The dimensionality reduction, together with the strong preferential alignment properties, leads to new dynamical insights for understanding and modelling the role of the anisotropic pressure Hessian in three-dimensional turbulent flows.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Intermittency
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A38
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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