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Expanding the Q–R space to three dimensions

Published online by Cambridge University Press:  10 December 2009

BEAT LÜTHI ,
MARKUS HOLZNER  and
ARKADY TSINOBER
BEAT LÜTHI*
Affiliation:
International Collaboration for Turbulence Research Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Strasse 15, 8093 Zurich, Switzerland
MARKUS HOLZNER
Affiliation:
International Collaboration for Turbulence Research Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Strasse 15, 8093 Zurich, Switzerland
ARKADY TSINOBER
Affiliation:
International Collaboration for Turbulence Research School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
*
†Email address for correspondence: luethi@ifu.baug.ethz.ch
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Abstract

The two-dimensional space spanned by the velocity gradient invariants Q and R is expanded to three dimensions by the decomposition of R into its strain production −1/3sijsjkski and enstrophy production 1/4ωiωjsij terms. The {Q; R} space is a planar projection of the new three-dimensional representation. In the {Q; −sss; ωωs} space the Lagrangian evolution of the velocity gradient tensor Aij is studied via conditional mean trajectories (CMTs) as introduced by Martín et al. (Phys. Fluids, vol. 10, 1998, p. 2012). From an analysis of a numerical data set for isotropic turbulence of Reλ ~ 434, taken from the Johns Hopkins University (JHU) turbulence database, we observe a pronounced cyclic evolution that is almost perpendicular to the Q–R plane. The relatively weak cyclic evolution in the Q–R space is thus only a projection of a much stronger cycle in the {Q; −sss; ωωs} space. Further, we find that the restricted Euler (RE) dynamics are primarily counteracted by the deviatoric non-local part of the pressure Hessian and not by the viscous term. The contribution of the Laplacian of Aij, on the other hand, seems the main responsible for intermittently alternating between low and high intensity Aij states.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 497 - 507
Copyright
Copyright © Cambridge University Press 2009

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