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Structure Functions in Complex Flows

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Abstract

The turbulence in the ocean and atmosphere is most of the time non-homogeneous in nature. These spatial changes could affect the structure of the turbulence. In this work a classification is proposed to determine the intermittency and mixing ability. The variation of the structure functions and the scaling exponent in decaying non-homogeneous turbulence produced by a grid and by a jet is measured with a sonic velocimeter SONTEK3-D. We use Extended Self Similarity (ESS) to obtain better estimates of the scaling exponents of the structure functions of order up to the 6th. We study the variation of the absolute scaling exponents ζp and relative scaling exponents ¯ζp as a function of distance from the source of turbulence. In most cases, the absolute scaling exponent ζ3 is shown to vary as function of the separation distance l. On the other hand the relative scaling exponents ¯ζp depend on the location of the flow and in most cases the deviations from the Kolmogorov 1941 scaling are related to the intermittency.

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References

  1. Sreenivasan, K.R. and Antonia, R.A., The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29 (1997) 435–472.

    Google Scholar 

  2. Frisch, U., Turbulence: The Legacy of A.N. Kolmogorov, 1995. Cambridge University Press, Cambridge (1995).

    Google Scholar 

  3. Kolmogorov, A.N., Dissipation of energy in locally isotropic turbulence. C. R. Acad. Sci. USSR 32 (1941) 16–18.

    Google Scholar 

  4. Anselmet, F., Gagne, Y., Hopfinger, E.J. and Antonia, R.A., High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140 (1984) 63–89.

    Google Scholar 

  5. Vincent, A. and Meneguzzi, M., The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225 (1991) 1–25.

    Google Scholar 

  6. Kolmogorov, A.N., A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13 (1962) 82–85.

    Google Scholar 

  7. She, Z.S. and Leveque, E., Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72 (1994) 336–339.

    Google Scholar 

  8. Frisch, U., Sulem, P.L. and Nelkin, M., A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87 (1978) 719–736.

    Google Scholar 

  9. Benzi, R., Ciliberto, S., Baudet, C., Chavarria, G.R. and Tripiccione, R., Extended self-similarity in the dissipative range of fully developed turbulence. Europhys. Lett. 24 (1993) 275–279.

    Google Scholar 

  10. Stolovitzky, G. and Sreenivasan, K.R., Scaling of structure functions. Phys. Rev. E 48(1) (1993) 32–36.

    Google Scholar 

  11. Taylor, G.Y., The spectrum of turbulence. Proc. R. Soc. A 164 (1938) 476–490.

    Google Scholar 

  12. Benzi, R., Ciliberto, S., Baudet, C. and Chavarria, G.R., On the scaling of three-dimensional homogeneous and isotropic turbulence. Physica D 80 (1995) 385–398.

    Google Scholar 

  13. Benzi, R., Biferale, L., Ciliberto, S., Struglia, M.V. and Tripiccione, R., Generalized scaling in fully developed turbulence. Physica D 96 (1996) 162–181.

    Google Scholar 

  14. Benzi, R., Ciliberto, S., Tripiccione, R., Massaioli, F. and Succi, S., Extended self-similarity in turbulent flows. Phys. Rev. E 48 (1993) 29–36.

    Google Scholar 

  15. Babiano, A., Dubrulle, B. and Frick, P., Scaling properties of two dimensional turbulence. Phys. Rev. E 52(4) (1995) 3719–3729.

    Google Scholar 

  16. Babiano, A., Dubrulle, B. and Frick, P., Some properties of two-dimensional inverse energy cascade dynamics. Phys. Rev. E 55(3) (1997) 2693–2706.

    Google Scholar 

  17. Dubrulle, B., Intermittency in fully developed turbulence. Phys. Rev. Lett. 73 (1994) 959–962.

    Google Scholar 

  18. Pinton, J.F. and Labbé, R., Correction to the Taylor hypothesis in swirling flows. J. Phys. II France 4 (1994) 1461–1468.

    Google Scholar 

  19. Herweijer, J.A., The small-scale structure of turbulence. Ph.D. Thesis, University of Eindhoven (1995).

  20. Protas, B., Goujon-Durand, S. and Wesfreid, J.E., Scaling properties of two-dimensional turbulence in wakes behind bluf bodies. Phys. Rev. E. 55(3) (1997) 1–5.

    Google Scholar 

  21. Gaudin, E., Goujon-Durand, S., Protas, B., Wesfreid, J.E. and Wojciechowski, J., Spatial properties of velocity structure functions in turbulent wake flows. Phys. Rev. E 57 (1998) 9–12.

    Google Scholar 

  22. Monin, A.S. and Yaglom, A.M., Statistical Fluid Mechanics, Vol. 2, MIT Press, Cambridge, MA (1975).

    Google Scholar 

  23. Redondo, J.M., Turbulencia y mezcla en dinamica de fluidos geofisicos. UPC, Barcelona (1995) p. 53.

    Google Scholar 

  24. Favre, A., Kovasznay, L.S.G., Dumas, R., Gaviglio, J. and Coantic, M., La turbulence en mécanique des fluides. BORDAS, Paris (1976).

    Google Scholar 

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Mahjoub, O., Redondo, J. & Babiano, A. Structure Functions in Complex Flows. Flow, Turbulence and Combustion 59, 299–313 (1997). https://doi.org/10.1023/A:1001199825354

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