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An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number

Published online by Cambridge University Press:  15 February 2007

MICHELE GUALA ,
ALEXANDER LIBERZON ,
ARKADY TSINOBER  and
WOLFGANG KINZELBACH
MICHELE GUALA
Affiliation:
Institute of Environmental Engineering, Swiss Federal Institute of Technology, ETH Zurich, CH-8093 Zurich, Switzerland
ALEXANDER LIBERZON
Affiliation:
Institute of Environmental Engineering, Swiss Federal Institute of Technology, ETH Zurich, CH-8093 Zurich, Switzerland Department of Fluid Mechanics and Heat Transfer, Tel Aviv University, 69978 Tel Aviv, Israel
ARKADY TSINOBER
Affiliation:
Marie Curie Chair in Fundamental and Conceptual Aspects of Turbulent Flows, Institute for Mathematical Sciences and Department of Aeronautics, Imperial College, London SW7 2AZ, UK
WOLFGANG KINZELBACH
Affiliation:
Institute of Environmental Engineering, Swiss Federal Institute of Technology, ETH Zurich, CH-8093 Zurich, Switzerland
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Abstract

Lagrangian auto- and cross-correlation functions of the rate of strain s2, enstrophy ω2, their respective production terms −sijsjkski and ωiωjsij, and material derivatives, Ds2/Dt and Dω2/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Reλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensor sij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2 to the relatively shorter time scales of s2, ωiωjsij and −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s2 and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkski and s2 and between −sijsjkski and Ds2/Dt, in addition to a marked anti-correlation between ωiωjsij and Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s2 and its production term, −sijsjkski.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 574 , 10 March 2007 , pp. 405 - 427
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Andreotti, B., Douady, S. & Couder, Y. 2001 An experiment on two aspects of the interaction between strain and vorticity. J. Fluid Mech. 444, 151–174.CrossRefGoogle Scholar
Brachet, M. E., Meneguzzi, M., Vincent, A., Politano, H. & Sulem, P. L. 1992 Numerical evidence of smooth self-similar dynamics and possibility of subsequent collapse for three-dimensional ideal flows. Phys. Fluids A 4, 2845–2854.CrossRefGoogle Scholar
Cao, N., Chen, S. & Doolen, G. D. 1999 Statistics and structures of pressure in isotropic turbulence. Phys. Fluid. 11, 2235–2250.CrossRefGoogle Scholar
Chacin, J. & Cantwell, B. J. 2000 Dynamics of a low Reynolds number turbulent boundary layer. J. Fluid Mech. 404, 87–115.CrossRefGoogle Scholar
Chong, M. S. & Perry, A. E. 1990 A general classification of three dimensional flow fields. Phys. Fluids A 2, 765–777.CrossRefGoogle Scholar
Constantin, P. 1994 Geometric statistics in turbulence. SIAM Rev. 36, 73–98.CrossRefGoogle Scholar
Guala, M., Lüthi, B., Liberzon, A., Kinzelbach, W. & Tsinober, A. 2005 On the evolution material lines and vorticity in homogeneous turbulence. J. Fluid Mech. 533, 339–359.CrossRefGoogle Scholar
Jeong, E. & Girimaji, X. 2003 Velocity gradient dynamics in turbulence: effect of viscosity and forcing. J. Theor. Comput. Fluid Dyn. 16, 421–432.CrossRefGoogle Scholar
Jimenez, J. & Wray, A. A. 1998 On the characteristic of vortex filaments in isotropic turbulence. J. Fluid Mech. 373, 255–285.CrossRefGoogle Scholar
Kholmyansky, M., Tsinober, A. & Yorish, S. 2001 Velocity derivatives in the atmospheric surface layer at Re λ = 104. Phys. Fluid. 13, 311–314.CrossRefGoogle Scholar
Lüthi, B. 2002 Some aspects of strain, vorticity and material element dynamics as measured with three-dimensional particle tracking velocimetry in a turbulent flow. PhD Dissertation, Swiss Federal Institute of Technology, ETHZ.Google Scholar
Lüthi, B., Tsinober, A. & Kinzelbach, W. 2005 Lagrangian measurement of vorticity dynamics in turbulent flow. J. Fluid Mech. 528, 87–118.CrossRefGoogle Scholar
Martin, J. N., Ooi, A., Chong, M. S. & Soria, J. 1998 Dynamics of the velocity gradient tensor invariants in isotropic turbulence. Phys. Fluid. 10, 2336–2346.CrossRefGoogle Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, The Mechanics of Turbulence, New English edition vol. 1, Chapters 2 and 3. CTR Monographs, NASA Ames – Stanford University.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, The Mechanics of Turbulence, vol. 2. CTR Monographs, NASA Ames – Stanford University.Google Scholar
Mordant, N., Leveque, E. & Pinton, J. F. 2004 Experimental and numerical study on the Lagrangian dynamics of high Reynolds turbulence. New J. Phys. 6, 116.CrossRefGoogle Scholar
Nomura, K. K. & Post, G. K. 1998 The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence. J. Fluid Mech. 377, 65–97.CrossRefGoogle Scholar
Ooi, A., Martin, J. N., Chong, M. S. & Soria, J. 1999 A study of the evolution and characteristics of the invariants of the velocity gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141–174.CrossRefGoogle Scholar
Pope, S. B. 1990 Lagrangian microscales in turbulence. Phil. Trans. R. Soc. Lond. 333, 309–319.Google Scholar
Priestley, M. B. 1981 Spectral Analysis and Time Series. Academic.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. R. Soc. Lond. A 100, 114–121.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in turbulence. MIT Press.CrossRefGoogle Scholar
Tsinober, A. 2000 Vortex stretching versus production of strain/dissipation. In Turbulence Structure and Vortex Dynamics (ed. Hunt, J. C. R. & Vassilicos, J. C.), pp. 164–191. Cambridge University Press.Google Scholar
Tsinober, A. 2001 An Informal Introduction to Turbulence. Kluwer.CrossRefGoogle Scholar
Vincent, A. & Meneguzzi, M. 1994 The dynamics of vorticity tubes in homogeneous turbulence. J. Fluid Mech. 258, 245–254.CrossRefGoogle Scholar
Yeung, P. K. 2001 Lagrangian characteristics of turbulence and scalar transport in direct numerical simulation. J. Fluid Mech. 427, 24–274.CrossRefGoogle Scholar
Yeung, P. K. 2002 Lagrangian investigation of turbulence. Annu. Rev. Fluid Mech. 34, 115–142.CrossRefGoogle Scholar
Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulation of isotropic turbulence. J. Fluid Mech. 207, 531–586.CrossRefGoogle Scholar
Zeff, B. W., Lanterman, D. D., McAllister, R., Rajarshi, R., Kostelich, E. J. & Lathrop, P. 2004 Measuring intense rotation and dissipation in turbulent flows. Nature 421 146–149.CrossRefGoogle Scholar