Homogeneity constraints on the mixed moments of velocity gradient and pressure Hessian in incompressible turbulence

Zhideng Zhou and Ping-Fan Yang
Phys. Rev. Fluids 8, 024601 – Published 3 February 2023

Abstract

In homogeneous turbulent flow, a relation for the correlation between velocity gradient mijuixj and pressure Hessian hijp2pxixj was found recently: tr(mhpm)=12(tr(m2))2. We discuss the implications of this relation to the velocity gradient dynamics: together with the Poisson equation for pressure, the homogeneity relation yields an identity between (tr(m2))2 and the integration of a two-point fourth-order correlation function of velocity gradient for isotropic flows. Our results indicate that the main contributions to tr(mhpm) come from scales less than roughly 20 times the Kolmogorov scale. Also, the homogeneity relation provides restrictions to the parameters in the closure models of pressure Hessian in velocity gradient dynamics. We further discuss the generalization of this homogeneity relation to turbulent shear flows, and we show numerically that this relation between tr(mhpm) and (tr(m2))2 is approximately satisfied even in the presence of a shear and of a wall, as it occurs in turbulent channel flows.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 25 October 2022
  • Accepted 17 January 2023

DOI:https://doi.org/10.1103/PhysRevFluids.8.024601

©2023 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Zhideng Zhou1,2 and Ping-Fan Yang1,2,3,*

  • 1The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
  • 2School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 3Center for Combustion Energy and Department of Energy and Power Engineering, Tsinghua University, 100084 Beijing, China

  • *Corresponding author: yangpingfan@imech.ac.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 8, Iss. 2 — February 2023

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Fluids

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×