Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence

Journal of Fluid Mechanics

Volumn 654, Issue , 2010, Pages 233-270

  Yang, Yue ^a   Pullin, D I ^a   Bermejo Moreno, Iávn ^a  

^a California Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY; HIGH ENERGY PHYSICS; TURBULENCE; VELOCITY; VORTEX FLOW;

ADVECTION EQUATIONS; DIFFERENT LENGTH SCALE; ISOTROPIC TURBULENCE; LAGRANGIAN STRUCTURES; MULTI-SCALE GEOMETRIC ANALYSIS; STATISTICAL GEOMETRY; TOPOLOGY PRESERVING; TURBULENT VELOCITY FIELDS;

LAGRANGE MULTIPLIERS;

ADVECTION; EULERIAN ANALYSIS; GEOMETRY; LAGRANGIAN ANALYSIS; TURBULENCE; TURBULENT FLOW; VORTEX;

EID: 77957115289     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010000571     Document Type: Article

References (52)

1. Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1-21.
2. 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, 2343-2353.
3. Batchelor, G. K. 1952a Diffusion in a field of homogeneous turbulence. Part II. The relative motion of particles. Proc. Cambridge Phil. Soc. 48, 345-362.
4. Batchelor, G. K. 1952b The effect of homogeneous turbulence on material lines and surfaces. Proc. R. Soc. Lond. A 213, 349-366.
5. Bermejo-Moreno, I. & Pullin, D. I. 2008 On the non-local geometry of turbulence. J. Fluid Mech. 603, 101-135.
6. Bermejo-Moreno, I., Pullin, D. I. & Horiuti, K. 2009 Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence. J. Fluid Mech. 620, 121-166.
7. Boratav, O. N. & Pelz, R. B. 1994 Direct numerical simulation of transition to turbulence from a high-symmetry initial condition. Phys. Fluids 6, 2757-2784.
8. Bourgoin, M., Ouellette, N. T., Xu, H. T., Berg, J. & Bodenschatz, E. 2006 The role of pair dispersion in turbulent flow. Science 311, 835-838.
9. Brachet, M. E., Meiron, D. I., Orszag, S. A., Nickel, B. G., Morf, R. H. & Frisch, U. 1983 Small-scale structure of the Taylor-Green vortex. J. Fluid Mech. 130, 411-452.
10. Brethouwer, G., Hunt, J. C. R. & Nieuwstadt, F. T. M. 2003 Micro-structure and Lagrangian statistics of the scalar field with a mean gradient in isotropic turbulence. J. Fluid Mech. 474, 193-225.
11. Candès, E., Demanet, L., Donoho, D. & Ying, L. 2005 Fast discrete curvelet transforms. Multiscale Model Simul. 5, 861-899.
12. Chertkov, M., Pumir, A. & Shraiman, B. I. 1999 Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11, 2394-2410.
13. Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765-777.
14. Chung, D. & Pullin, D. I. 2009 Large-eddy simulation and wall modelling of turbulent channel flow. J. Fluid Mech. 631, 281-309.
15. Demanet, L. & Ying, L. 2007 Curvelets and wave atoms for mirror-extended images. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol.6701, p. 67010J. SPIE.
16. Farge, M. 1992 Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395-457.
17. Girimaji, S. S. & Pope, S. B. 1990 Material-element deformation in isotropic turbulence. J. Fluid Mech. 220, 427-458.
18. Goto, S. & Kida, S. 2007 Reynolds-number dependence of line and surface stretching in turbulence: folding effects. J. Fluid Mech. 586, 59-81.
19. Haller, G. 2001 Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149, 248-277.
20. Hou, T. Y. & Li, R. 2006 Computing nearly singular solutions using pseudo-spectral methods. J. Comput. Phys. 226, 379-397.
21. Kraichnan, R. H. 1965 Lagrangian-history closure approximation for turbulence. Phys. Fluids 8, 575-598.
22. Leonard, A. 2009 The universal structure of high-curvature regions of material lines in chaotic flows. J. Fluid Mech. 622, 167-175.
23. LeVeque, R. J. 1992 Numerical Methods for Conservation Laws, 2nd edn. Birkḧauser.
24. Li, Y. & Meneveau, C. 2007 Material deformation in a restricted Euler model for turbulent flows: analytic solution and numerical tests. Phys. Fluids 19, 015104.
25. Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 2193-2203.
26. Ma, J., Hussaini, M. Y., Vasilyev, O. V. & Le Dimet, F.-X. 2009 Multiscale geometric analysis of turbulence by curvelets. Phys. Fluids 21, 075104.
27. Marsden, J. E. & Hughes, T. J. R. 1994 Mathematical Foundations of Elasticity. Dover.
28. Meneveau, C. 1991 Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech. 232, 469-520.
29. Misra, A. & Pullin, D. I. 1997 A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9, 2443-2454.
30. Moisy, F. & Jiménez, J. 2004 Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111-133.
31. Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics of Turbulence. MIT.
32. Nahum, A. & Seifert, A. 2006 Technique for backward particle tracking in a flow field. Phys. Rev. E 74, 016701.
33. Peng, J. & Dabiri, J. O. 2008 An overview of a Lagrangian method for analysis of animal wake dynamics. J. Exp. Biol. 211, 280-287.
34. Pope, S. B. 1987 Turbulent premixed flames. Annu. Rev. Fluid Mech. 19, 237-270.
35. Pope, S. B., Yueng, P. K. & Girimaji, S. S. 1989 The curvature of material surfaces in isotropic turbulence. Phys. Fluids A 1, 2010-2018.
36. Pullin, D. I. & Saffman, P. G. 1993 On the Lundgren-Townsend model of turbulent fine scales. Phys. Fluid A 5, 126-145.
37. Pumir, A., Shraiman, B. I. & Chertkov, M. 2000 Geometry of Lagrangian dispersion in turbulence. Phys. Rev. Lett. 85, 5324-5327.
38. Rhines, P. B. & Young, W. R. 1983 How rapidly is a passive scalar mixed within closed streamlines? J. Fluid Mech. 133, 133-145.
39. Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601-639.
40. Ruetsch, G. R. & Maxey, M. R. 1992 The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluid A 4, 2747-2760.
41. Salazar, J. P. L. C. & Collins, L. R. 2009 Two-particle dispersion in isotropic turbulent flows. Annu. Rev. Fluid Mech. 41, 405-432.
42. Sawford, B. 2001 Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289-317.
43. Schumacher, J., Sreenivasan, K. R. & Yeung, P. K. 2005 Very fine structures in scalar mixing. J. Fluid Mech. 531, 113-122.
44. Stam, J. 1999 Stable fluids. In SIGGRAPH'99: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, pp. 121-128. ACM.
45. Taylor, G. I. 1922 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196-212.
46. Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375-404.
47. Wang, L. P. & Peters, N. 2006 The length-scale distribution function of the distance between extremal points in passive scalar turbulence. J. Fluid Mech. 554, 457-475.
48. Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203-240.
49. Xu, H., Ouellette, N. T. & Bodenschatz, E. 2008 Evolution of geometric structures in intense turbulence. New J. Phys. 10, 013012.
50. Yang, Y., He, G.-W. & Wang, L.-P. 2008 Effects of subgrid-scale modelling on Lagrangian statistics in large-eddy simulation. J. Turbul. 9 (8), 1-24.
51. Yeung, P. K. 2002 Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech. 34, 115-142.
52. Yeung, P. K. & Pope, S. B. 1988 An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence. J. Comput. Phys. 79, 373-416.