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Statistical properties of pressure-Hessian tensor in a turbulent channel flow

Published online by Cambridge University Press:  18 January 2022

Jiu-Peng Tang ,
Zhen-Hua Wan Open the ORCID record for Zhen-Hua Wan [Opens in a new window] ,
Nan-Sheng Liu Open the ORCID record for Nan-Sheng Liu [Opens in a new window]  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Jiu-Peng Tang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, PR China
Zhen-Hua Wan*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Nan-Sheng Liu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
*
†Email addresses for correspondence: wanzh@ustc.edu.cn, xlu@ustc.edu.cn
†Email addresses for correspondence: wanzh@ustc.edu.cn, xlu@ustc.edu.cn
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Abstract

A direct numerical simulation database of a weakly compressible turbulent channel flow with bulk Mach number 1.56 is studied in detail, including the geometrical relationships between the pressure-Hessian tensor and the vorticity/strain-rate tensor, as well as the mechanism of the pressure-Hessian tensor contributing to the evolution of invariants of the velocity gradient tensor. The results show that the geometrical relationships between the pressure-Hessian tensor and the vorticity/strain-rate tensor in the central region of the channel are consistent with that of isotropic turbulence. However, in the buffer layer with relatively stronger inhomogeneity and anisotropy, the vorticity tends to be aligned with the first or second eigenvector of the pressure-Hessian tensor in the unstable focus/compressing topological region, and tends to be aligned with the first eigenvector of the pressure-Hessian tensor in the stable focus/stretching topological region. In the unstable node/saddle/saddle and stable node/saddle/saddle topological regions, the vorticity prefers to lie in the plane of the first and second eigenvectors of the pressure-Hessian tensor. The strain-rate and the pressure-Hessian tensors tend to share their second principal direction. Moreover, for the coupling between the pressure-Hessian tensor and the principal strain rates, we clarify the influence on dissipation, the nonlinear generation of dissipation and the enstrophy generation. The decomposition of the pressure-Hessian tensor further shows that the slow pressure-related term dominates the pressure-Hessian tensor's contribution, and the influence of inhomogeneity and anisotropy mainly originates from the inhomogeneity and anisotropy of the fluctuating velocity. These statistical properties would be instructive in formulating dynamical models of the velocity gradient tensor for wall turbulence.

JFM classification

Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A22
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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