The geometrical properties of streamline segments (Wang, 2010 [1]) and their bounding surface (Schaefer et al., 2012 [2]) in direct numerical simulations (DNS) of different types of turbulent flows at different Reynolds numbers are reviewed. Particular attention is paid to the geometrical relation of the bounding surface and local and global extrema of the instantaneous turbulent kinetic energy field. Also a previously derived model equation for the normalized probability density of the length of streamline segments is reviewed and compared with the new data. It is highlighted that the model is Reynolds number independent when normalized with the mean length of streamline segments yielding that the mean length plays a paramount role as the only relevant length scale in the pdf. Based on a local expansion of the field of the absolute value of the velocity u along the streamline coordinate a scaling of the mean size of extrema of u is derived which is then shown to scale with the mean length of streamline segments. It turns out that scales with the geometrical mean of the Kolmogorov scale η and the Taylor microscale λ so that . The new scaling is confirmed based on the DNS cases over a range of Taylor based Reynolds numbers of .
Philip Schäfer 1 ; Markus Gampert 1 ; Norbert Peters 1
@article{CRMECA_2012__340_11-12_859_0,
author = {Philip Sch\"afer and Markus Gampert and Norbert Peters},
title = {On the scaling of the mean length of streamline segments in various turbulent flows},
journal = {Comptes Rendus. M\'ecanique},
pages = {859--866},
publisher = {Elsevier},
volume = {340},
number = {11-12},
year = {2012},
doi = {10.1016/j.crme.2012.10.032},
language = {en},
}
TY - JOUR AU - Philip Schäfer AU - Markus Gampert AU - Norbert Peters TI - On the scaling of the mean length of streamline segments in various turbulent flows JO - Comptes Rendus. Mécanique PY - 2012 SP - 859 EP - 866 VL - 340 IS - 11-12 PB - Elsevier DO - 10.1016/j.crme.2012.10.032 LA - en ID - CRMECA_2012__340_11-12_859_0 ER -
%0 Journal Article %A Philip Schäfer %A Markus Gampert %A Norbert Peters %T On the scaling of the mean length of streamline segments in various turbulent flows %J Comptes Rendus. Mécanique %D 2012 %P 859-866 %V 340 %N 11-12 %I Elsevier %R 10.1016/j.crme.2012.10.032 %G en %F CRMECA_2012__340_11-12_859_0
Philip Schäfer; Markus Gampert; Norbert Peters. On the scaling of the mean length of streamline segments in various turbulent flows. Comptes Rendus. Mécanique, Volume 340 (2012) no. 11-12, pp. 859-866. doi : 10.1016/j.crme.2012.10.032. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.10.032/
[1] On properties of fluid turbulence along streamlines, J. Fluid Mech., Volume 648 (2010), pp. 183-203
[2] The length distribution of streamline segments in homogeneous isotropic decaying turbulence, Phys. Fluids, Volume 24 (2012), p. 045104
[3] The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR, Volume 30 (1941), pp. 301-305
[4] Turbulence: The Legacy of A.N. Kolmogorov, Cambridge University Press, 1995
[5] Random geometric problems suggested by turbulence (M. Rosenblatt; C. van Atta, eds.), Statistical Models and Turbulence, Lecture Notes in Physics, vol. 12, Springer Verlag, 1971, pp. 300-316
[6] Intermittent vortex structures in homogeneous isotropic turbulence, Nature, Volume 344 (1990), pp. 226-228
[7] High-resolution direct numerical simulation of turbulence, J. Turbulence, Volume 7 (2006), pp. 1-17
[8] The length scale distribution function of the distance between extremal points in passive scalar turbulence, J. Fluid Mech., Volume 554 (2006), pp. 457-475
[9] Length scale distribution functions and conditional means for various fields in turbulence, J. Fluid Mech., Volume 608 (2008), pp. 113-138
[10] Fine structure of scalar fields mixed by turbulence. I. Zero gradient points and minimal gradient surfaces, Phys. Fluids, Volume 11 (1968), pp. 2305-2315
[11] Testing of different model equations for the mean dissipation using Kolmogorov flows, Flow Turbul. Combust., Volume 85 (2010), pp. 225-243
[12] Geometry of streamlines in fluid flow theory, Def. Sci. J., Volume 28 (1978), pp. 175-178
[13] Geometry of particle paths in turbulent flows, J. Turbul., Volume 7 (2006), pp. 1-10
[14] Geometric properties of particle trajectories in turbulent flows, J. Turbul., Volume 12 (2011)
[15] Curvature statistics of streamlines in various turbulent flows, J. Turbul., Volume 13 (2012) no. 1, p. 28
[16] Acceleration statistics as measures of statistical persistence of streamlines in isotropic turbulence, Phys. Rev. E, Volume 71 (2005)
[17] Particle pair diffusion and persistent streamline topology in two-dimensional turbulence, New J. Phys., Volume 6 (2004), p. 65
[18] Topological visualisation of focal structures in free shear flows, Appl. Sci. Res., Volume 53 (1994), pp. 375-386
[19] Asymptotic analysis of homogeneous isotropic decaying turbulence with unknown initial conditions, J. Turbul., Volume 12 (2011), pp. 1-20
[20] Extensive strain along gradient trajectories in the turbulent kinetic energy field, New J. Phys., Volume 13 (2011), p. 043012
[21] P. Schaefer, M. Gampert, N. Peters, Joint statistics and conditional mean strain rates of streamline segments, Phys. Scr. T (2012), in press.
[22] M. Gampert, P. Schaefer, J. Goebbert, N. Peters, Decomposition of the field of the turbulent kinetic energy into regions of compressive and extensive strain, Phys. Scr. T (2012), in press.
[23] Mathematical analysis of random noise, Bell Syst. Tech. J., Volume 23 (1944) no. 282
[24] Mathematical analysis of random noise, Bell Syst. Tech. J., Volume 24 (1945) no. 46
[25] Dissipation of energy under locally isotropic turbulence, Dokl. Akad. Nauk SSSR, Volume 32 (1941), pp. 16-18
[26] Eulerian and Lagrangian time microscales in isotropic turbulence, J. Fluid Mech., Volume 67 (1975), pp. 561-567
Cité par Sources :
Commentaires - Politique