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Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface

Published online by Cambridge University Press:  23 October 2009

MARKUS HOLZNER ,
B. LÜTHI ,
A. TSINOBER  and
W. KINZELBACH
MARKUS HOLZNER*
Affiliation:
International Collaboration for Turbulence Research Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Strasse 15, 8093 Zurich, Switzerland
B. LÜTHI
Affiliation:
International Collaboration for Turbulence Research Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Strasse 15, 8093 Zurich, Switzerland
A. TSINOBER
Affiliation:
International Collaboration for Turbulence Research School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel Institute for Mathematical Sciences and Department of Aeronautics, Imperial College, London SW7 2AZ, UK
W. KINZELBACH
Affiliation:
International Collaboration for Turbulence Research Institute of Environmental Engineering, ETH Zurich, Wolfgang-Pauli-Strasse 15, 8093 Zurich, Switzerland
*
†Email address for correspondence: holzner@ifu.baug.ethz.ch
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Abstract

This paper presents an analysis of flow properties in the proximity of the turbulent/non-turbulent interface (TNTI), with particular focus on the acceleration of fluid particles, pressure and related small scale quantities such as enstrophy, ω2 = ωiωi, and strain, s2 = sijsij. The emphasis is on the qualitative differences between turbulent, intermediate and non-turbulent flow regions, emanating from the solenoidal nature of the turbulent region, the irrotational character of the non-turbulent region and the mixed nature of the intermediate region in between. The results are obtained from a particle tracking experiment and direct numerical simulations (DNS) of a temporally developing flow without mean shear. The analysis reveals that turbulence influences its neighbouring ambient flow in three different ways depending on the distance to the TNTI: (i) pressure has the longest range of influence into the ambient region and in the far region non-local effects dominate. This is felt on the level of velocity as irrotational fluctuations, on the level of acceleration as local change of velocity due to pressure gradients, Du/Dt ≃ ∂u/∂t ≃ −∇ p/ρ, and, finally, on the level of strain due to pressure-Hessian/strain interaction, (D/Dt)(s2/2) ≃ (∂/∂t)(s2/2) ≃ −sijp,ij > 0; (ii) at intermediate distances convective terms (both for acceleration and strain) as well as strain production −sijsjkski > 0 start to set in. Comparison of the results at Taylor-based Reynolds numbers Reλ = 50 and Reλ = 110 suggests that the distances to the far or intermediate regions scale with the Taylor microscale λ or the Kolmogorov length scale η of the flow, rather than with an integral length scale; (iii) in the close proximity of the TNTI the velocity field loses its purely irrotational character as viscous effects lead to a sharp increase of enstrophy and enstrophy-related terms. Convective terms show a positive peak reflecting previous findings that in the laboratory frame of reference the interface moves locally with a velocity comparable to the fluid velocity fluctuations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 639 , 25 November 2009 , pp. 153 - 165
Copyright
Copyright © Cambridge University Press 2009

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