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Comparative study of vorticity and material lines evolution in numerical turbulence. (English) Zbl 1143.76029

Summary: A comparative study of differences in the evolution processes of vorticity and material lines based on DNS of NSE is performed at low Reynolds number \(Re_\lambda \approx 50\) for time periods up to 15 Kolmogorov microscales. In order to observe such differences, we looked for regions in which the forcing and viscous terms are approximately balancing each other (in the sense as defined in the main text), and used the Lagrangian tracking of fluid particles originating from these regions for time periods during which the above balance between the forcing and the viscous terms remain valid.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
Full Text: DOI

References:

[1] Alvelius, K.: Random forcing of three-dimensional homogeneous turbulence. Phys. Fluids 11, (7), 1880–1889 (1999) · Zbl 1147.76306 · doi:10.1063/1.870050
[2] Biferale, L., Lanotte, A.S., Toschi, F.: Effects of forcing in three-dimensional turbulent flows. Phys. Rev. Lett. 9, 094503 (2004) · Zbl 1086.76020 · doi:10.1103/PhysRevLett.92.094503
[3] Busa, J., Hnatich, M., Honkonen, J., Horvath, D.: Stability of Kolmogorov scaling in anisotropically forced turbulence. Phys. Rev. E55, (1), 381–394 (1997)
[4] Chen, S., Shan, X.: High-resolution turbulent simulations using the Connection Machine-2. Comput. Phys. 6, (6), 643–646 (1992) · doi:10.1063/1.168444
[5] Eswaran, V., Pope, S.B.: An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16, 257–278 (1988) · Zbl 0662.76069 · doi:10.1016/0045-7930(88)90013-8
[6] Galanti, B., Tsinober, A.: Self-amplification of the field of velocity derivatives in quasi-isotropic turbulence. Phys. Fluids 12, (12), 3097–3099 (2000) · Zbl 1184.76170 · doi:10.1063/1.1320830
[7] Galanti, B., Gendler-Fishman, D., Liberzon, A., Tsinober, A.: Comparative study of disturbances: vorticity vs. material lines. In: Fridrich, R., et al. (eds.) Proceedings of 5th International Symposium on Turbulence and Shear Flow Phenomena, vol. 2., pp. 545–548. Munich (2007)
[8] Galanti, B., Gendler-Fishman, D., Tsinober, A.: Comparative study of vorticity and material lines evolution in numerical turbulence – the role of forcing. In: Hanjalić, K., Nagano, Y., Jakirlic, S. (eds.) Turbulence, Heat and Mass Transfer 5. Proceeding of The International Symposium on Turbulence, Heat and Mass Transfer, pp. 105–108 · Zbl 1143.76029
[9] Galanti, B., Gendler-Fishman, D., Tsinober, A.: Is it possible to study Euler (or inviscid/purely inertial) evolution in low Reynolds number flows? In: Palma and Lopes (eds.) Springer proceedings in physics, vol. 117, Advances in turbulence XI, pp. 17–19 (2007)
[10] Galanti, B., Tsinober, A.: Physical space properties of helicity in quasi-homogeneous forced turbulence. Phys. Lett. A352, (1–2), 141–149 (2006) · Zbl 1187.76681
[11] Gendler-Fishman, D.: Comparative study of vorticity and material lines evolution in numerical turbulence. Ph.D. thesis. Tel-Aviv University, Israel (2008) · Zbl 1143.76029
[12] Girimaji, S.S., Pope, S.B.: Material-element deformation in isotropic turbulence. J. Fluid Mech. 220, 427–458 (1990) · Zbl 0697.76071 · doi:10.1017/S0022112090003330
[13] Guala, M., Lüthi, B., Liberzon, A., Tsinober, A., Kinzelbach, W.: On the evolution of material lines and vortex lines in homogeneous turbulence. J. Fluid Mech. 533, 339–359 (2005) · Zbl 1114.76301 · doi:10.1017/S0022112005004362
[14] Huang, M.J.: Correlations of vorticity and material line elements with strain in decaying turbulence. Phys. Fluids 8, 2203–2214 (1996) · doi:10.1063/1.868993
[15] Kuczaj, A.K., Geurts, B.J.: Mixing in manipulated turbulence. J. Turbul. 7, (67), 1–28 (2006) · Zbl 1273.76247 · doi:10.1080/14685240600827534
[16] Kuz’min, G.A.: Ideal incompressible hydro dynamics in terms of the vortex momentum density. Phys. Lett., A 96, 88–90 (1983) · doi:10.1016/0375-9601(83)90597-2
[17] Liberzon, A., Guala, M., Lüthi, B., Tsinober, A., Kinzelbach, W.: Turbulence in dilute polymer solutions. Phys. Fluids 17, 031707/1–031707/5 (2005) · Zbl 1187.76312
[18] Lundgren, T.S.: Linearly forced isotropic turbulence. Annual Research Briefs, Center for Turbulence Research, pp. 461–473 (2003)
[19] Lüthi, B., Tsinober, A., Kinzelbach, W.: Lagrangian measurement of vorticity dynamics in turbulent flow. J. luid Mech. 528, 87–118 (2005) · Zbl 1154.76303 · doi:10.1017/S0022112004003283
[20] Machiels, L., Deville, M.O.: Numerical simulation of randomly forced turbulent flows. J. Comput. Phys. 145, 246–279 (1998) · Zbl 0926.76086 · doi:10.1006/jcph.1998.6006
[21] Mazzi, B., Vassilicos, J.C.: Fractal generated turbulence. J. Fluid Mech. 502, 65–87 (2004) · Zbl 1134.76362 · doi:10.1017/S0022112003007249
[22] Mordant, N., Leveque, E., Pinton, J.-F.: Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence. New J. Phys. 6, 116/1–116/44 (2004) · doi:10.1088/1367-2630/6/1/116
[23] Oseledets, V.I.: On a new way of writing the Navier–Stokes equation: the Hamiltonian formalism. Russ. Math. Surv. 44, 210–211 (1989) · Zbl 0850.76130 · doi:10.1070/RM1989v044n03ABEH002122
[24] Overholt, M.R., Pope, S.B.: A deterministic forcing scheme for direct numerical simulations of turbulence. Comput. Fluids 27, (1), 11–28 (1998) · Zbl 0908.76071 · doi:10.1016/S0045-7930(97)00019-4
[25] Rosales, C., Meneveau, C.: Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17, 095106/1–095106/8 (2005) · Zbl 1187.76449 · doi:10.1063/1.2047568
[26] Sullivan, N.P., Mahalingam, S., Kerr, R.: Deterministic forcing of homogeneous, isotropic turbulence. Phys. Fluids 6, (4), 1612–1614 (1994) · doi:10.1063/1.868274
[27] Tennekes, H.: Eulerian and Lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67, 561–567 (1975) · Zbl 0302.76033 · doi:10.1017/S0022112075000468
[28] Tennekes, H., Lumley, J.L.: A First Course of Turbulence. MIT Press, Cambridge, MA (1972) · Zbl 0285.76018
[29] Tsinober, A.: An Informal Introduction to Turbulence. Kluwer, Norwell, MA (2001) · Zbl 1137.76025
[30] Tsinober, A.: How analogous is generation of vorticity and passive vector (magnetic fields). In: Molokov, S., et al. (eds.) Magnetohydrodynamics: Evolution of Ideas and Trends. Springer, Berlin (2006)
[31] Yeung, P.K.: One- and two-particle Lagrangian acceleration correlations in numerically simulated homogeneous turbulence. Phys. Fluids 9, 2981–2990 (1997) · doi:10.1063/1.869409
[32] Yeung, P.K.: Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech. 34, 115–142 (2002) · Zbl 1047.76027 · doi:10.1146/annurev.fluid.34.082101.170725
[33] Yeung, P.K., Pope, S.B.: An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence. J. Comput. Phys. 79, 373–416 (1988) · Zbl 0655.76042 · doi:10.1016/0021-9991(88)90022-8
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