Experimental assessment of fractal scale similarity in turbulent flows. Part 3. Multifractal scaling

Journal of Fluid Mechanics

Volumn 338, Issue , 1997, Pages 127-155

  Frederiksen, Richard D ^a   Dahm, Werner J A ^a   Dowling, David R ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CASCADES (FLUID MECHANICS); ENERGY DISSIPATION; FRACTALS; GEOMETRY; REYNOLDS NUMBER; STATISTICAL METHODS;

BILINEAR MULTIPLIER DISTRIBUTION; FRACTAL SCALE SIMILARITY (FSS); MULTIFRACTAL SCALING;

TURBULENT FLOW;

FRACTAL; SCALING; TURBULENT FLOW;

FLOW MODELLING; FRACTAL PROPERTIES; TURBULENT FLOW;

EID: 0031131539     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096004089     Document Type: Article

References (38)

1. BATCHELOR, G. K. 1959 Small-scale variation of convected quantities like temperature in a turbulent fluid. J. Fluid Mech. 5, 113-139.
2. BENZI, R., PALADIN, G., PARISI, G. & VULPIANI, A. 1984 On the multifractal nature of fully developed turbulence and chaotic systems. J. Phys. A: Math. Nucl. Gen. 17, 3521-3531.
3. BOHR, T. & RAND, D. 1987 The entropy function for characteristic exponents. Physica D 25, 387-398.
4. CHECHETKIN, V. R., LUTOVINOV, V. S. & TURYGIN, A. Y. 1990 Multifractal structure of fully developed hydrodynamic turbulence. II. Intermittency effects in the distribution of passive scalar impurities. J. Stat. Phys. 61, 589-605.
5. CHHABRA, A. B. & SREENIVASAN, K. R. 1992 Scale invariant multiplier distributions in turbulence. Phys. Rev. Lett. 68, 2762-2765.
6. COLLET, P., LEBOWITZ, J. L. & PORZIO, A. 1987 The dimension spectrum of some dynamical system. J. Stat. Phys. 47, 609-644.
7. DAHM, W. J. A., SOUTHERLAND, K. B. & BUCH, K. A. 1991 Direct, high-resolution, four-dimensional measurements of the fine scale structure of Sc ≫ 1 molecular mixing in turbulent flows. Phys. Fluids A 3, 1115-1127.
8. FALCONER, K. 1990 Fractal Geometry: Mathematical Foundations and Applications. John Wiley.
9. FREDERIKSEN, R. D., DAHM, W. J. A. & DOWLING, D. R. 1996 Experimental assessment of fractal scale similarity in turbulent flows. Part 1. One-dimensional intersections. J. Fluid Mech. 327, 35-72.
10. FREDERIKSEN, R. D., DAHM, W. J. A. & DOWLING, D. R. 1997 Experimental assessment of fractal scale similarity in turbulent flows. Part 2. Higher-dimensional intersections and non-fractal inclusions. J. Fluid Mech. 338, 89-126.
11. FRISCH, U. & PARISI, G. 1985 In Turbulence and Predictability in Geophysical Fluid Mechanics and Climate Dynamics (ed. M. Ghil, R. Benzi & G. Parisi). North-Holland.
12. FRISCH, U., SULEM, P. & NELKIN, M. 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719-736.
13. HALSEY, T. C., JENSEN, M. H., KADANOFF, L. P., PROCACCIA, I. & SHRAIMAN, B. I. 1986 Fractal measures and their singularities: The characterization of strange sets. Phys. Rev. A 33, 1141-1151.
14. HENTSCHEL. H. G. E. & PROCACCIA, I. 1983 The infinite number of generalized dimensions of fractals and strange attractors. Physica D 8, 435-444.
15. JIMÉNEZ, J., WRAY, A. A., SAFFMAN, P. G. & ROGALLO, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65-90.
16. MANDELBROT, B. B. 1974 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62. 331-358.
17. MANDELBROT, B. B. 1990 Negative fractal dimensions and multifractals. Physica A 163, 306-315.
18. MANDELBROT, B. B. 1991 Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism. Proc. R. Soc. Lond. A 434, 79-88.
19. MENEVEAU, C. 1991 Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech. 232, 469-520.
20. MENEVEAU, C. & SREENIVASAN, K. R. 1987 Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett. 59, 1424-1427.
21. MENEVEAU, C. & SREENIVASAN, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429-484.
22. OTT, E. & ANTONSEN, T. M. 1989 Fractal measures of passively convected vector fields and scalar gradients in chaotic fluid flows. Phys. Rev. A 39, 3660-3671.
23. OTT, E., GREBOGI, C. & YORKE, J. A. 1989 Theory of first order phase transitions for chaotic attractors of nonlinear dynamical systems. Phys. Lett. A 135, 343-348.
24. PEITGEN, H., JURGEN, H. & SAUPE, D. 1992 Chaos and Fractals: New Frontiers of Science. Springer.
25. PRASAD, R. R., MENEVEAU, C. & SREENIVASAN, K. R. 1988 The multifractal nature of the dissipation field of passive scalars in fully turbulent flows. Phys. Rev. Lett. 61, 74-77.
26. PRASAD, R. R. & SREENIVASAN, K. R. 1990 Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows. J. Fluid Mech. 216, 1-34.
27. SHIVAMOGGI, B. K. 1992 Multi-fractal aspects of the intermittency corrections to the spectrum of temperature fluctuations in isotropic turbulence. Phys. Lett. A 168, 47-54.
28. SOUTHERLAND, K. B. & DAHM, W. J. A. 1994 A four-dimensional experimental study of conserved scalar mixing in turbulent flows. Report No. 026779-12, Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI.
29. SOUTHERLAND, K. B. & DAHM, W. J. A. 1996 Fully resolved four-dimensional measurements of the small-scale structure of passive scalar mixing in turbulent flows. Submitted to J. Fluid Mech.
30. SOUTHERLAND, K. B., DAHM, W. J. A. & DOWLING, D. R. 1995 Experimental results for the high wavenumber spectral structure of scalar mixing in turbulent shear flows. In Proc. 10th Symp. Turb. Shear Flows, Pennsylvania State University, University Park, PA.
31. SREENIVASAN, K. R. 1991a Fractals and multifractals in fluid turbulence. Ann. Rev. Fluid Mech. 23, 539-600.
32. SREENIVASAN, K. R. 1991b On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165-182.
33. SREENIVASAN, K. R. & PRASAD, R. R. 1989 New results on the fractal and multifractal structure of the large Schmidt number passive scalars in fully turbulent flows. Physica D 38, 322-329.
34. SREENIVASAN, K. R. & STOLOVITZKY, G. 1995 Turbulent cascades. J. Stat. Phys. 78, 311-333.
35. SU, L. K. & DAHM, W. J. A. 1996a Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows. Part I: Assessment of errors. Phys. Fluids 8, 1869-1882.
36. SU, L. K. & DAHM, W. J. A. 1996b Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows. Part II: Experimental results. Phys. Fluids 8, 1883-1906.
37. TSINOBER, A., KIT, E. & DRACOS, T. 1992 Experimental investigation of the field of velocity gradients in turbulent flows. J. Fluid Mech. 242, 169-192.
38. VARÓSI, F., ANTONSEN, T. M. & OTT, E. 1991 The spectrum of fractal dimensions of passively convected scalar gradients in chaotic fluid flows. Phys. Fluids A 3, 1017-1028.