Experimental assessment of fractal scale-similarity in turbulent flows. Part 1. One-dimensional intersections

Journal of Fluid Mechanics

Volumn 327, Issue , 1996, Pages 35-72

  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

DIFFUSION IN LIQUIDS; ENERGY DISSIPATION; FRACTALS; RANDOM PROCESSES; SPATIAL VARIABLES MEASUREMENT;

FRACTAL SCALE SIMILARITY; ONE DIMENSIONAL INTERSECTIONS;

TURBULENT FLOW;

FRACTALS; MODELLING-MATHEMATICAL; TURBULENT FLOW;

EID: 0030294643     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096008452     Document Type: Article

References (33)

1. BATCHELOR, G. K. 1959 Small-scale variation of convected quantities like temperature in 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. BEVINGTON, P. R. & ROBINSON, D. K. 1992 Data Reduction and Error Analysis in the Physical Sciences. McGraw-Hill.
4. 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.
5. DOWLING, D. R. 1991 The estimated scalar dissipation rate in gas-phase turbulent jets. Phys. Fluids A 3, 2229-2246.
6. DUBUC, B., QUINIOU, J. F., ROQUES-CARMES, C., TRICOT, C. & ZUCKER, S. W. 1989 Evaluating the fractal dimension of profiles. Phys. Rev. A 39, 1500-1512.
7. FEDER, J. 1988 Fractals. Plenum Press.
8. FREDERIKSEN, R. D., DAHM, W. J. A. & DOWLING, D. R. 1997 a Experimental assessment of fractal scale similarity in turbulent flows. Part 2. Higher-dimensional intersections and non-fractal inclusions. J. Fluid Mech. (to appear).
9. FREDERIKSEN, R. D., DAHM, W. J. A. & DOWLING, D. R. 1997b Experimental assessment of fractal scale similarity in turbulent flows. Part 3. Multifractal scaling. J. Fluid Mech. (to appear).
10. 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.
11. FRISCH, U., SULEM, P. L. & NELKIN, M. 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719-736.
12. GRASSBERGER, P. 1983 Generalized dimensions of strange attractors. Phys. Lett. A 97, 227-230.
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. KOLMOGOROV, A. N. 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. C.R. Acad. Sci. URSS 30, 301-305.
17. LANE-SERFF, G. F. 1993 Investigation of the fractal structure of jets and plumes. J. Fluid Mech. 249, 521-534.
18. 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.
19. MANDELBROT, B. B. 1982 The Fractal Geometry of Nature. W. H. Freeman and Company, New York.
20. MENEVEAU, C. & SREENIVASAN, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429-484.
21. MILLER, P. L. & DIMOTAKIS, P. E. 1991 Stochastic geometric properties of scalar interfaces in turbulent jets. Phys. Fluids A 3, 168-177.
22. 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.
23. PRASAD, R. R. & SREENIVASAN, K. R. 1990 The measurement and interpretation of fractal dimensions of the scalar interface in turbulent flows. Phys. Fluids A 2, 792-807.
24. PRESS, W. H., TEUKOLSKY, S. A., VETTERLING, W. T. & FLANNERY, B. P. 1992 Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge University Press, Cambridge.
25. RICHARDSON, S. F. 1920 The supply of energy from and to atmospheric eddies. Proc. R. Soc. Lond. A 97, 354-373.
26. SOUTHERLAND, K. B. & DAHM, W. J. A. 1994 A four-dimensional experimental study of conserved scalar mixing in turbulent flows. Rep. 026779-12. Department of Aerospace Engineering, The University of Michigan.
27. 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. Turbulent Shear Flows. Pennsylvania State University, University Park, PA.
28. SREENIVASAN, K. R. 1991 Fractals and multifractals in fluid turbulence. Ann. Rev. Fluid Mech. 23, 539-600.
29. SREENIVASAN, K. R. & MENEVEAU, C. 1986 The fractal facets of turbulence. J. Fluid Mech. 173, 357-386.
30. 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.
31. SREENIVASAN, K. R., RAMSHANKAR, R. & MENEVEAU, C. 1989 Mixing, entrainment and fractal dimension of surfaces in turbulent flows. Proc. R. Soc. Lond. A 421, 79-108.
32. TAYLOR, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421-478.
33. THEILER, J. 1990 Estimating fractal dimension. J. Opt. Soc. Am. A 7, 1055-1073.