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On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars

Published online by Cambridge University Press:  29 March 2006

Benoit B. Mandelbrot
Benoit B. Mandelbrot
Affiliation:
General Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598
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Abstract

This paper studies several geometric aspects of the Poisson and Gaussian random fields approximating Burgers k−2 and Kolmogorov $k^{-\frac{5}{3}}$ homogeneous turbulence. In particular, simulated sample scalar iso-surfaces (e.g. surfaces of constant temperature or concentration) are exhibited, and their relative degrees of wiggliness are shown to be best characterized by saying that the corresponding fractal dimensions are respectively equal to 3−½ and $3-\frac{1}{3}$.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 3 , 9 December 1975 , pp. 401 - 416
Copyright
© 1975 Cambridge University Press

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