Effects of SGS stresses on velocity gradient dynamics

C. Meneveau, F. van der Bos, B. Tao, J. Katz

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

The effects of small-scale motions on the inertial range structure of turbulence are investigated by considering the dynamics of the velocity gradient tensor filtered at inertial-range scales. In addition to self-interactions and the filtered pressure Hessian, the evolution of the filtered velocity gradient tensor is determined by the subgrid-scale stress tensor. As in so-called Restricted Euler dynamics, the evolution equations can be simplified by considering two invariants R and Q. The effects of the subgrid-scale stress tensor on them can be quantified unambiguously by evaluating conditional averages that appear in the evolution equation for the joint PDF of the invariants. The required conditional averages are computed from three-dimensional HPIV measurements of fully developed turbulence in a square duct, at a friction Reynolds number of about 2300. The results show that the SGS stresses have significant effects, e.g. along the so-called Vieillefosse tail they oppose the formation of a finite-time singularity that occurs in Restricted Euler dynamics. A-priori tests of the Smagorinsky, nonlinear, and mixed models show that all reproduce the real SGS stress effect along the Vieillefosse tail, but that they fail in several other regions. An attempt is made to optimize the mixed model by letting the two coefficients be functions of the two invariants R and Q.
Original languageEnglish
Title of host publicationBAPS, procedings of the 54th Annual Meeting APS Division of Fluid Dynamics
Pages-
Publication statusPublished - 18 Nov 2002

Publication series

NameBulletin of the American Physical Society
Number9
Volume47
ISSN (Print)0003-0503

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gradients
stress tensors
turbulence
tensors
dimensional measurement
ducts
Reynolds number
friction
coefficients
interactions

Keywords

  • METIS-211938

Cite this

Meneveau, C., van der Bos, F., Tao, B., & Katz, J. (2002). Effects of SGS stresses on velocity gradient dynamics. In BAPS, procedings of the 54th Annual Meeting APS Division of Fluid Dynamics (pp. -). (Bulletin of the American Physical Society; Vol. 47, No. 9).
Meneveau, C. ; van der Bos, F. ; Tao, B. ; Katz, J. / Effects of SGS stresses on velocity gradient dynamics. BAPS, procedings of the 54th Annual Meeting APS Division of Fluid Dynamics. 2002. pp. - (Bulletin of the American Physical Society; 9).
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Meneveau, C, van der Bos, F, Tao, B & Katz, J 2002, Effects of SGS stresses on velocity gradient dynamics. in BAPS, procedings of the 54th Annual Meeting APS Division of Fluid Dynamics. Bulletin of the American Physical Society, no. 9, vol. 47, pp. -.

Effects of SGS stresses on velocity gradient dynamics. / Meneveau, C.; van der Bos, F.; Tao, B.; Katz, J.

BAPS, procedings of the 54th Annual Meeting APS Division of Fluid Dynamics. 2002. p. - (Bulletin of the American Physical Society; Vol. 47, No. 9).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

TY - GEN

T1 - Effects of SGS stresses on velocity gradient dynamics

AU - Meneveau, C.

AU - van der Bos, F.

AU - Tao, B.

AU - Katz, J.

PY - 2002/11/18

Y1 - 2002/11/18

N2 - The effects of small-scale motions on the inertial range structure of turbulence are investigated by considering the dynamics of the velocity gradient tensor filtered at inertial-range scales. In addition to self-interactions and the filtered pressure Hessian, the evolution of the filtered velocity gradient tensor is determined by the subgrid-scale stress tensor. As in so-called Restricted Euler dynamics, the evolution equations can be simplified by considering two invariants R and Q. The effects of the subgrid-scale stress tensor on them can be quantified unambiguously by evaluating conditional averages that appear in the evolution equation for the joint PDF of the invariants. The required conditional averages are computed from three-dimensional HPIV measurements of fully developed turbulence in a square duct, at a friction Reynolds number of about 2300. The results show that the SGS stresses have significant effects, e.g. along the so-called Vieillefosse tail they oppose the formation of a finite-time singularity that occurs in Restricted Euler dynamics. A-priori tests of the Smagorinsky, nonlinear, and mixed models show that all reproduce the real SGS stress effect along the Vieillefosse tail, but that they fail in several other regions. An attempt is made to optimize the mixed model by letting the two coefficients be functions of the two invariants R and Q.

AB - The effects of small-scale motions on the inertial range structure of turbulence are investigated by considering the dynamics of the velocity gradient tensor filtered at inertial-range scales. In addition to self-interactions and the filtered pressure Hessian, the evolution of the filtered velocity gradient tensor is determined by the subgrid-scale stress tensor. As in so-called Restricted Euler dynamics, the evolution equations can be simplified by considering two invariants R and Q. The effects of the subgrid-scale stress tensor on them can be quantified unambiguously by evaluating conditional averages that appear in the evolution equation for the joint PDF of the invariants. The required conditional averages are computed from three-dimensional HPIV measurements of fully developed turbulence in a square duct, at a friction Reynolds number of about 2300. The results show that the SGS stresses have significant effects, e.g. along the so-called Vieillefosse tail they oppose the formation of a finite-time singularity that occurs in Restricted Euler dynamics. A-priori tests of the Smagorinsky, nonlinear, and mixed models show that all reproduce the real SGS stress effect along the Vieillefosse tail, but that they fail in several other regions. An attempt is made to optimize the mixed model by letting the two coefficients be functions of the two invariants R and Q.

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Meneveau C, van der Bos F, Tao B, Katz J. Effects of SGS stresses on velocity gradient dynamics. In BAPS, procedings of the 54th Annual Meeting APS Division of Fluid Dynamics. 2002. p. -. (Bulletin of the American Physical Society; 9).