Scale Distributions and Fractal Dimensions in Turbulence.

A new geometric framework connecting scale distributions to coverage statistics is employed to analyze level sets arising in turbulence as well as in other phenomena. A 1D formalism is described and applied to Poisson, lognormal, and power-law statistics. A d-dimensional generalization is also presented. Level sets of 2D spatial measurements of jet-fluid concentration in turbulent jets are analyzed to compute scale distributions and fractal dimensions. Lognormal statistics are used to model the level sets at inner scales. The results are in accord with data from other turbulent flows.

[1]  Raúl E. López,et al.  The Lognormal Distribution and Cumulus Cloud Populations , 1977 .

[2]  K. Sreenivasan.  FRACTALS AND MULTIFRACTALS IN FLUID TURBULENCE , 1991 .

[3]  M. Longuet-Higgins.  On the intervals between successive zeros of a random function , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  H. Takayasu.  Differential Fractal Dimension of Random Walk and Its Applications to Physical Systems , 1982 .

[5]  B. M. Fulk.  MATH , 1992 .

[6]  D. Mark,et al.  Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping , 1984 .

[7]  A. Kolmogorov.  A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number , 1962, Journal of Fluid Mechanics.

[8]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[9]  Paul E. Dimotakis,et al.  Mixing in turbulent jets: scalar measures and isosurface geometry , 1996, Journal of Fluid Mechanics.

[10]  Roddam Narasimha,et al.  Zero-crossings in turbulent signals , 1983, Journal of Fluid Mechanics.

[11]  Eugene Yee,et al.  Measurements of level-crossing statistics of concentration fluctuations in plumes dispersing in the atmospheric surface layer , 1995 .

[12]  L. Welling,et al.  Fractal analysis and imaging of the proximal nephron cell. , 1996, The American journal of physiology.

[13]  최인후,et al.  13 , 1794, Tao te Ching.

[14]  P. Dimotakis,et al.  Stochastic geometric properties of scalar interfaces in turbulent jets , 1991 .

[15]  B. Mandelbrot.  Fractal Geometry of Nature , 1984 .

[16]  Constantin,et al.  Fractal geometry of isoscalar surfaces in turbulence: Theory and experiments. , 1991, Physical review letters.

[17]  K. Sreenivasan,et al.  Zero crossings of velocity fluctuations in turbulent boundary layers , 1993 .

[18]  G. Cherbit,et al.  Fractals: Non-Integral Dimensions and Applications , 1991 .