Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T07:41:42.713Z Has data issue: false hasContentIssue false
  • English
  • Français

On properties of fluid turbulence along streamlines

Published online by Cambridge University Press:  07 April 2010

LIPO WANG
LIPO WANG*
Affiliation:
Institut für Technische Verbrennung, RWTH-Aachen, 52056 Aachen, Germany
*
†Present address: UM-SJTU Joint Institute, ShangHai JiaoTong University, 800 Dong Chuan Road, 200240 Shanghai, China. Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Geometrical and dynamical properties of turbulent flows have been investigated by streamline segment analysis. Starting from each grid point, a streamline segment is defined as the part of its streamline bounded by the two adjacent extremal points of the velocity magnitude. Physically the streamline segments can be extended into a more meaningful concept, namely the streamtube segments, which are non-overlapping and space filling. This decomposition of the flow allows for new insights into vector-related statistics in turbulence. According to the variation of velocity, the streamline segments can be sorted into positive and negative segments. The overall properties of turbulent flows can be newly understood and explained from the statistics of these segments with simple structures; for instance, the negative skewness of the velocity derivative becomes naturally a kinematic outcome. Furthermore, from direct numerical simulations conditional statistics of pressure and kinetic energy dissipation along the streamline segments are evaluated and discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 183 - 203
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aivazis, K. A. & Pullin, D. I. 2001 On velocity structure functions and the spherical vortex model for isotropic turbulence. Phys. Fluids 13 (7), 2019–2029.CrossRefGoogle Scholar
Batchelor, G. K. & Townsend, A. A. 1947 Decay of vorticity in isotropic turbulence. Proc. R. Soc. A 190, 534–550.Google Scholar
Boffetta, G., Celani, A. & Vegassola, M. 2000 Inverse energy cascade in two-dimensional turbulence: deviations from Gaussian behaviour. Phys. Rev. E 61 (1), 29–32.CrossRefGoogle Scholar
Braun, W., Lillo, F. D. & Eckhardt, B. 2006 Geometry of particle paths in turbulent flows. J. Turbul. 7 (62), 1–10.CrossRefGoogle Scholar
Brons, M. 2007 Streamline topology: patterns in fluid flows and their bifurcations. Adv. Appl. Mech. 41, 1C43.Google Scholar
Chen, L., Goto, S. & Vassilicos, J. C. 2006 Turbulent clustering of stagnation points and inertial particles. J. Fluid Mech. 553, 143C154.Google Scholar
Davey, A. 1961 Boundary-layer flow at a saddle point of attachment. J. Fluid Mech. 10, 593–610.Google Scholar
Davila, J. & Vassilicos, J. C. 2003 Richard's pair diffusion and the stagnation point structure of turbulence. Phys. Rev. Lett. 91 (14), 144501.CrossRefGoogle Scholar
George, W. K., Beuther, P. D. & Arndt, R. E. A. 1984 Pressure spectra in turbulent free shear flows. J. Fluid Mech. 148, 155–191.Google Scholar
Gotoh, T. & Fukayama, D. 2001 Pressure spectrum in homogeneous turbulence. Phys. Rev. Lett. 86 (17), 3775–3778.Google Scholar
Gotoh, T. & Rogallo, R. 1999 Intermittency and scaling of pressure at small scales in forced isotropic turbulence. J. Fluid Mech. 396, 257–285.CrossRefGoogle Scholar
Hamman, C., Klewicki, J. & Kirby, R. 2008 On the Lamb vector divergence in Navier–Stokes flows. J. Fluid Mech 610, 261–284.CrossRefGoogle Scholar
Kalelkar, C. 2006 Statistics of pressure fluctuations in decaying isotropic turbulence. Phys. Rev. E 73, 046301.Google Scholar
Kaneda, Y. & Ishihara, T. 2006 High-resolution direct numerical simulation of turbulence. J. Turbul. 7 (20), 1–17.Google Scholar
Li, Y. & Meneveau, C. 2006 Intermittency trends and Lagrangian evolution of non-Gaussian statistics in turbulent flow and scalar transport. J. Fluid Mech. 558, 133–142.CrossRefGoogle Scholar
Lighthill, M. J. 1963 Attachment and separation in three-dimensional flow. Laminar Boundary Layers (ed. Rosenhead, L.). 2.6, 72–82. Oxford University Press.Google Scholar
Lin, C. C. 1953 On Taylor's hypothesis and the acceleration terms in the Navier–Stokes equations. Quart. Appl. Math. 10, 295–306.Google Scholar
Lumley, J. L. & Yaglom, A. M. 2001 A century of turbulence. Flow Turbul. Combust. 66, 241–286.Google Scholar
Mellado, J. P., Wang, L. & Peters, N. 2009 Gradient trajectory analysis of a scalar field with external intermittency. J. Fluid Mech. 626, 333–365.CrossRefGoogle Scholar
Moffatt, H. K., Kida, S. & Ohkitain, K. 1994 Stretched vortices: the sinews of turbulence; large-Reynolds-number asymptotics. J. Fluid Mech. 259, 241–264.Google Scholar
Moffatt, H. K. & Tsinober, A. 1992 Helicity in laminar and turbulent flow. Annu. Rev. Fluid Mech. 24, 281–312.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press.Google Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155.Google Scholar
Petrila, T. & Trif, D. 2005 Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics. Springer.Google Scholar
Rao, P. 1978 Geometry of streamlines in fluid flow theory. Def. Sci. J. 28 (4), 175–178.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–39.Google Scholar
Rotta, J. C. 1972 Turbulente Strömungen. B. G. Teubner Stuttgart.Google Scholar
She, Z. S., Jackson, E & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226–228.CrossRefGoogle Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435C72.CrossRefGoogle Scholar
Synge, J. L. & Lin, C. C. 1943 On a statistical model of isotropic turbulence. Trans. R. Soc. Can. 37, 45–79.Google Scholar
Taylor, G. I. 1938 Production and dissipation of vorticity in a turbulent fluid. Proc. R. Soc. A 164, 15–23.Google Scholar
Tsinober, A., Vedulab, P. & Yeung, P. K. 2001 Random Taylor hypothesis and the behaviour of local and convective accelerations in isotropic turbulence. Phys. Fluids 13, 1974–1984.Google Scholar
Vedula, P. & Yeung, P. K. 1999 Similarity scaling of acceleration and pressure statistics in numerical simulations of isotropic turbulence. Phys. Fluids 11 (5), 1208–1220.Google Scholar
Wang, L. & Peters, N. 2006 The length-scale distribution function of the distance between extremal points in passive scalar turbulence. J. Fluid Mech. 554, 457–475.CrossRefGoogle Scholar
Wang, L. & Peters, N. 2008 Length-scale distribution functions and conditional means for various fields in turbulence. J. Fluid Mech. 608, 113–138.Google Scholar
Wang, L. 2008 Geometrical description of homogeneous shear turbulencce using dissipation element analysis. PhD thesis, Shaker, Germany.Google Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–40.Google Scholar
Yannacopoulos, A. N., Rowlands, G. & King, G. P. 2002 A Melnikov function for the breakup of closed streamlines in steady Navier–Stokes flows. Phys. Fluids 14 (5), 1572–1579.Google Scholar