Fractal dimensions and spectra of interfaces with application to turbulence
Abstract
An analysis is presented of any convoluted surface in two or three dimensions which has a self-similar structure, and which may simply be defined as a mathematical surface or as an interface where there is a sharp change in the value of a scalar field. A distinction is drawn between two types of self-similarity which is pertinent for problems of interfaces in fluid flows: a local and a global self-similarity. It is demonstrated that interfaces with a localized self-similar structure around accumulation points, such as spirals, may have noninteger capacities D(K) and D-prime(K) even though their Hausdorff dimension is integer and equal to the topological dimension of the surface. It is explained how the same surface can have different values of D(K) and D-prime(K) over different asymptotic ranges of epsilon.
- Publication:
-
Proceedings of the Royal Society of London Series A
- Pub Date:
- December 1991
- DOI:
- 10.1098/rspa.1991.0158
- Bibcode:
- 1991RSPSA.435..505V
- Keywords:
-
- Computational Fluid Dynamics;
- Fluid Boundaries;
- Fractals;
- Liquid-Liquid Interfaces;
- Turbulent Flow;
- Asymptotes;
- High Reynolds Number;
- Kolmogoroff Theory;
- Power Spectra;
- Fluid Mechanics and Heat Transfer