TY - JOUR

T1 - Expanding the Q-R space to three dimensions

AU - Lthi, Beat

AU - Holzner, Markus

AU - Tsinober, Arkady

PY - 2009/12

Y1 - 2009/12

N2 - 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; s} space the Lagrangian evolution of the velocity gradient tensor Aij is studied via conditional mean trajectories (CMTs) as introduced by Martn 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 QR plane. The relatively weak cyclic evolution in the QR space is thus only a projection of a much stronger cycle in the {Q; sss;ωω s} 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.

AB - 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; s} space the Lagrangian evolution of the velocity gradient tensor Aij is studied via conditional mean trajectories (CMTs) as introduced by Martn 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 QR plane. The relatively weak cyclic evolution in the QR space is thus only a projection of a much stronger cycle in the {Q; sss;ωω s} 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.

KW - Dynamics

KW - Isotropic

KW - Theory

UR - http://www.scopus.com/inward/record.url?scp=76249114766&partnerID=8YFLogxK

U2 - 10.1017/S0022112009991947

DO - 10.1017/S0022112009991947

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AN - SCOPUS:76249114766

VL - 641

SP - 497

EP - 507

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -