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Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

  • IVÁN BERMEJO-MORENO (a1), D. I. PULLIN (a1) and KIYOSI HORIUTI (a2)

Abstract

We perform a multi-scale non-local geometrical analysis of the structures extracted from the enstrophy and kinetic energy dissipation-rate, instantaneous fields of a numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in a periodic box. Three different resolutions are considered: 2563, 5123 and 10243 grid points, with kmax approximately 1, 2 and 4, respectively, the same initial conditions and Reλ ≈ 77. This allows a comparison of the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from blob-like and moderately stretched tube-like shapes at the large scales to highly stretched sheet-like structures at the small scales. The intermediate scales show a predominance of tube-like structures for both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency towards structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 2563 grid resolution case (kmax ≈ 1) was unable to detect the predominance of highly stretched sheet-like structures at the smaller scales in both fields. The same non-local methodology for the study of the geometry of structures, but without the multi-scale decomposition, is applied to two scalar fields used by existing local criteria for the eduction of tube- and sheet-like structures in turbulence, Q and [Aij]+, respectively, obtained from invariants of the velocity-gradient tensor and alike in the 10243 case. This adds the non-local geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally, we introduce a new methodology for the study of proximity issues among structures of different fields, based on geometrical considerations and non-local analysis, by taking into account the spatial extent of the structures. We apply it to the four fields previously studied. Tube-like structures of Q are predominantly surrounded by sheet-like structures of [Aij]+, which appear at closer distances. For the enstrophy, tube-like structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented.

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Corresponding author

Email address for correspondence: ibermejo@caltech.edu

References

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Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30, 23432353.
Batchelor, G. K. & Townsend, A. A. 1949 The nature of turbulent motion at large wavenumbers. Proc. R. Soc. Lond. A 199, 238255.
Bermejo-Moreno, I. & Pullin, D. I. 2008 On the non-local geometry of turbulence. J. Fluid Mech. 603, 101135.
Bradshaw, P. & Koh, Y. M. 1981 A note on Poisson's equation for pressure in a turbulent flow. Phys. Fluids 24, 777.
Brasseur, J. G. & Wang, Q. 1992 Structural evolution of intermittency and anisotropy at different scales analyzed using three-dimensional wavelet transforms. Phys. Fluids A 4, 25382554.
Candès, E., Demanet, L., Donoho, D. & Ying, L. 2005 Fast discrete curvelet transforms. Multiscale Model Simul. 5, 861899.
Chen, S., Sreenivasan, K. R. & Nelkin, M. 1997 Inertial range scalings of dissipation and enstrophy in isotropic turbulence. Phys. Rev. Lett. 79, 12531256.
Goto, Susumu 2008 A physical mechanism of the energy cascade in homogeneous isotropic turbulence. J. Fluid Mech. 605, 355–266.
Hamlington, P. E., Schumacher, J. & Dahm, W. J. A. 2008 Local and nonlocal strain rate fields and vorticity alignment in turbulent flows. Phys. Rev. E 77, 026303.
He, G., Chen, S., Kraichan, R. H., Zhang, R. & Zhou, Y. 1998 Statistics of dissipation and enstrophy induced by localized vortices. Phys. Rev. Lett. 81, 4639.
Horiuti, K. 2001 A classification method for vortex sheet and tube structures in turbulent flows. Phys. Fluids A 13 (12), 37563774.
Horiuti, K. & Fujisawa, T. 2008 The multi-mode stretched spiral vortex in homogeneous isotropic turbulence. J. Fluid Mech. 595, 341366.
Horiuti, K. & Takagi, Y. 2005 Identification method for vortex sheet structures in turbulent flows. Phys. Fluids 17 (12), 121703.
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. Center for Turbulence Research Report CTR-S88.
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2003 Spectra of energy dissipation, enstrophy and pressure by high-resolution direct numerical simulations of turbulence in a periodic box. J. Phys. Soc. Japan 72, 983986.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Jiménez, J. 1992 Kinematic alignment effects in turbulent flows. Phys. Fluids A 4, 652654.
Jiménez, J., Wray, A. W., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 6590.
Kennedy, D. A. & Corrsin, S. 1961 Spectral flatness factor and intermittency in turbulence and in non-linear noise. J. Fluid Mech. 10, 366370.
Kerr, R. M. 1985 Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 3158.
Koenderink, J. J. & van Doorn, A. J. 1992 Surface shape and curvature scales. Image Vision Comput. 10 (8), 557565.
Kolmogorov, A. N. 1941 a Dissipation of energy in a locally isotropic turbulence. Dokl. Nauk. SSSR. 32, 1618.
Kolmogorov, A. N. 1941 b The local structure of turbulence in incompressible viscous fluids at very large Reynolds numbers. Dokl. Nauk. SSSR. 30, 301305.
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds numbers. J. Fluid Mech. 13, 8285.
Kraichnan, R. H. 1974 On Kolmogorov's inertial-range theories. J. Fluid Mech. 62, 305330.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 21932203.
Meneveau, C. 1991 Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech. 232, 469520.
Misra, A. & Pullin, D. I. 1997 A vortex-based subgrid stress model for large-eddy simulations. Phys. Fluids 9, 24432454.
Moisy, F. & Jiménez, J. 2004 Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111133.
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, 6597.
Okamoto, N., Yoshimatsu, K., Shneider, K., Farge, M. & Kaneda, Y. 2007 Coherent vortices in high resolution direct numerical simulation of homogeneous isotropic turbulence: A wavelet viewpoint. Phys. Fluids 19, 115109.
Onsager, L. 1945 The distribution of energy in turbulence. Phys. Rev. 68, 286.
Pullin, D. I. & Saffman, P. G. 1997 Vortex dynamics in turbulence. Annu. Rev. Fluid Mech. 30, 3151.
Richardson, L. F. 1922 Weather Prediction by Numerical Process. Cambridge University Press.
Richardson, L. F. 1926 Atmospheric diffusion shown on a distance-neighbor graph. Proc. R. Soc. Lond. Ser. A 110, 709737.
Ruetsch, G. R. & Maxey, M. R. 1992 The evolution of small-scale structures in isotropic homogeneous turbulence. Phys. Fluids A 4 (12), 27472760.
Schumacher, J., Sreenivasan, K. R. & Yeung, P. K. 2005 Very fine structures in scalar mixing. J. Fluid Mech. 531, 113122.
Siggia, E. D. 1981 Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375406.
Sreenivasan, K. R. 2004 Possible effects of small-scale intermittency in turbulent reacting flows. Flow, Turbul. Combus. 72, 115131.
Sreenivasan, K. R. & Meneveau, C. 1988 Singularities of the the equations of fluid motion. Phys. Rev. A 38, 62876295.
Tanaka, M. & Kida, S. 1993 Characterization of vortex tubes and sheets. Phys. Fluids A 5, 20792082.
Tao, B., Katz, J. & Meneveau, C. 2000 Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry. Phys. Fluids 12, 941944.
Tsinober, A., Kit, E. & Dracos, T. 1992 Experimental investigation of the field of velocity-gradients in turbulent flows. J. Fluid Mech. 242, 169192.
Vincent, A. & Meneguzzi, M. 1994 The dynamics of vorticity tubes in homogeneous turbulence. J. Fluid Mech. 258, 245254.
Wang, L. & Peters, N. 2006 The length-scale distribution function of the distance between extremal points in passive scalar turbulence. J. Fluid. Mech. 554, 457475.
Wu, J-Z., Zhou, Y. & Fan, M. 1999 A note on kinetic energy, dissipation and enstrophy. Phys. Fluids 11, 503505.
Zeff, B. W., Lanterman, D. D., McAllister, R., Roy, R., Kostelich, E. J. & Lathrop, D. P. 2003 Measuring intense rotation and dissipation in turbulent flows. Nature 421, 146149.
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Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

  • IVÁN BERMEJO-MORENO (a1), D. I. PULLIN (a1) and KIYOSI HORIUTI (a2)

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