Abstract
Using direct numerical simulation of turbulence in a periodic box driven by homogeneous forcing, with a maximum of 40963 grid points and Taylor micro-scale Reynolds numbers R λ up to 1131, it is shown that there is a transition in the forms of the significant, high vorticity, intermittent structures, from isolated vortices when R λ is less than 102 to complex thin-shear layers when R λ exceeds about 103. Both the distance between the layers and their widths are comparable with the integral length scale. The thickness of each of the layers is of the order of the Taylor micro-scale λ. Across the layers the velocity ‘jumps’ are of the order of the rms velocity u o of the whole flow. Within the significant layers, elongated vortical eddies are generated, with microscale thickness ℓ v ~10η ≪ λ, with associated peak values of vorticity as large as 35ω rms and with velocity jumps as large as 3.4u o , where η is the Kolmogorov micro scale and ω rms the rms vorticity. The dominant vortical eddies in the layers, which are approximately parallel to the vorticity averaged over the layers, are separated by distances of order ℓ v . The close packing leads to high average energy dissipation inside the layer, as large as ten times the mean rate of energy dissipation over the whole flow. The interfaces of the layers act partly as a barrier to the fluctuations outside the layer. However, there is a net energy flux into the small scale eddies within the thin layers from the larger scale motions outside the layer.
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References
Corrsin, S., Kistler, A.: Free-stream boundaries of turbulent flows. NACA Tech. Rep. 1244, pp. 1033–1064 (1955)
Bisset, D.K., Hunt, J.C.R., Rogers, M.M.: The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383 (2002)
Westerweel, J., Fukushima, C., Pedersen, J.M., Hunt, J.C.R.: Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199 (2009)
da Silva, C.B., dos Reis, R.: The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet. Phil. Trans. R. Soc. A 369, 738 (2011)
Ishihara, T., Gotoh, T., Kaneda, Y.: Study of high-reynolds number isotropic turbulence by direct numerical simulation. Annu. Rev. Fluid Mech. 41, 165 (2009)
Worth, N.A., Nickels, T.B.: Some characteristics of thin shear layers in homogeneous turbulent flow. Phil. Trans. R. Soc. A 369, 709 (2011)
Hunt, J., Eames, I., da Silva, C., Westerweel, J.: Interfaces and inhomogeneous turbulence. Phil. Trans. R. Soc. A 369, 811 (2011)
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K., Uno, A.: Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592, 335 (2007)
Aoyama, T., Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K., Uno, A.: Statistics of energy transfer in high-resolution direct numerical simulation of turbulence in a periodic box. J. Phys. Soc. Jpn. 74, 3202 (2005)
Kaneda, Y. (ed.): Computational Science of Turbulence. Kyoritsu Shuppan (2012)
Kerr, R.M.: Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31 (1985)
Vincent, A., Meneguzzi, M.: The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1 (1991)
Jiménez, J., Wray, A.A., Saffman, P.G., Rogallo, R.S.: The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65 (1993)
Yokokawa, M., Itakura, K., Uno, A., Ishihara, T., Kaneda, Y.: 16.4-tflops direct numerical simulation of turbulence by a fourier spectral method on the earth simulator. In: Proceeding of the IEEE/ACM SC2002 Conference, p. 50 (2002)
Kaneda, Y., Ishihara, T., Yokokawa, M., Itakura, K., Uno, A.: Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids 15, L21 (2003)
Balakrishnan, S.K., Thomas, T.G., Coleman, G.N.: Oblique interaction of a laminar vortex ring with a non-deformable free surface: vortex reconnection and breakdown. J. Phys. Conf. Ser. 318, 062002 (2011)
Kerr, R.M.: Swirling, turbulent vortex rings formed from a chain reaction of reconnection events. Phys. Fluids 25, 065101 (2013)
Bürger, K., Treib, M., Westermann, R., Werner, S., Lalescu, C.C., Szalay, A., Meneveau, C., Eyink, G.L.: Vortices within vortices: hierarchical nature of vortex tubes in turbulence. ArXiv:1210.3325 [physics.flu-dyn] (2012)
Dritschel, D.G., Haynes, P.H., Juckes, M.N., Shepherd, T.G.: The stability of a two-dimensional vorticity filament under uniform strain. J. Fluid Mech. 230, 647 (1991)
Hunt, J., Eames, I., Westerweel, J.: Vortical interactions with interfacial shear layers. In: Kaneda, Y. (ed.) Proceedings of IUTAM Conference on Computational Physics and New Perspectives in Turbulence, pp. 331–338. Springer (2008)
Kevlahan, N., Hunt, J.: Nonlinear interactions in turbulence with strong irrotational straining. J. Fluid Mech. 337, 333 (1997)
Tanahashi, K.F.M., Miyauchi, T.: Fine scale eddy cluster and energy cascade in homogeneous isotropic turbulence. In: Kaneda, Y. (ed.) Proceedings of IUTAM Conference on Computational Physics and New Perspectives in Turbulence, pp. 67–72. Springer (2008)
Hunt, J.C.R., Durbin, P.A.: Perturbed vortical layers and shear sheltering. Fluid Dyn. Res. 24, 375 (1999)
Richardson, L.F.: Weather Prediction by Numerical Process. Cambridge University Press (1922)
Kolmogorov, A.N.: Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16 (1941)
Cerutti, S., Meneveau, C.: Intermittency and relative scaling of subgrid-scale energy dissipation in isotropic turbulence. Phys. Fluids 10, 928 (1998)
Chen, Q., Chen, S., Eyink, G.L., Holm, D.D.: Intermittency in the joint cascade of energy and helicity. Phys. Rev. Lett. 90, 214503 (2003)
Domaradzki, J.A., Liu, W., Brachet, M.E.: An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence. Phys. Fluids A 5, 1747 (1993)
Gotoh, T., Watanabe, T.: Statistics of transfer fluxes of the kinetic energy and scalar variance. J. Turbul. 6, 1 (2005)
Piomelli, U., Cabot, W.H., Moin, P., Lee, S.: Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3, 1766 (1991)
Kerr, R.M., Domaradzki, J.A., Barbier, G.: Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence. Phys. Fluids 8, 197 (1996)
Anderson, B.W., Domaradzki, J.A.: A subgrid-scale model for large-eddy simulation based on the physics of interscale energy transfer in turbulence. Phys. Fluids 24, 065104 (2012)
Moisy, F., Jiménez, J.: Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111 (2004)
Batchelor, G.K., Townsend, A.A.: Nature of turbulent motion at large wave-numbers. Proc. Roy. Soc. Lond. A 199, 238 (1949)
Warhaft, Z.: Passive scalars in turbulent flows. Ann. Rev. Fluid Mech. 32, 203 (2000)
Hunt, J., Eames, I., Westerweel, J., Davidson, P.A., Voropayev, S., Fernando, J., Braza, M.: Thin shear layers - the key to turbulence structure? J. Hydro. Environ. Res. 4, 75 (2010)
Siggia, E.D.: Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375 (1981)
Miyauchi, T., Tanahashi, M.: Coherent fine scale structure in turbulence. In: Kambe, K., Nakano, T., Miyauchi T. (eds.) IUTAM Symposium on Geometry and Statistics of Turbulence, pp. 67–76. Kluwer (2001)
Ruetsch, G., Maxey, M.: The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluids A 4, 2747 (1992)
Fung, J.C.H.: Shear flow turbulence structure and its lagrangian statistics. Fluid Dyn. Res. 17, 147 (1996)
Argoul, F., Arneodo, A., Grasseau, G., Gagne, Y., Hopfinger, E.J., Frisch, U.: Wavelet analysis of turbulence reveals the multifractal nature of the richardson cascade. Nature 338, 51 (1989)
Obukhov, A.M.: Spectral energy distribution in a turbulent flow. Dokl. Akad. Nauk SSSR 32, 22 (1941)
Kolmogorov, A.N.: The local structure of turbulence in incompressible viscous fluid for very large reynolds number. C. R. Acad. Sci. URSS 30, 299 (1941)
Steinhoff, J., Underhill, D.: Modification of the euler equations for vorticity confinement: application to the computation of interacting vortex rings. Phys. Fluids 6(8), 2738 (1994)
Davidson, P.A.: On the decay of saffman turbulence subject to rotation, stratification or an imposed magnetic field. J. Fluid Mech. 663, 268 (2010)
Hunt, J., Carruthers, D.J.: Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497 (1990)
Ghosh, S., Davila, J., Hunt, J.C.R., Srdic, A., Fernando, H.J.S., Jonas, P.R.: How turbulence enhances coalescence of settling particles with applications to rain in clouds. Proc. Roy. Soc. A. 461, 3059 (2005)
Blum, D.B., Bewley, G.P., Bodenschatz, E., Gibert, M., Gylfason, A., Mydlarski, L., Voth, G.A., Xu, H., Yeung, P.K.: Signatures of non-universal large scales in conditional structure functions from various turbulent flows. New J. Phys. 13, 113020 (2011)
Williams, J.E.F., Purshouse, M.: A vortex sheet modelling of boundary-layer noise. J. Fluid Mech. 113, 187 (1981)
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Ishihara, T., Kaneda, Y. & Hunt, J.C.R. Thin Shear Layers in High Reynolds Number Turbulence—DNS Results. Flow Turbulence Combust 91, 895–929 (2013). https://doi.org/10.1007/s10494-013-9499-z
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DOI: https://doi.org/10.1007/s10494-013-9499-z