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 selfsimilar 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 selfsimilarity which is pertinent for problems of interfaces in fluid flows: a local and a global selfsimilarity. It is demonstrated that interfaces with a localized selfsimilar structure around accumulation points, such as spirals, may have noninteger capacities D(K) and Dprime(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 Dprime(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;
 LiquidLiquid Interfaces;
 Turbulent Flow;
 Asymptotes;
 High Reynolds Number;
 Kolmogoroff Theory;
 Power Spectra;
 Fluid Mechanics and Heat Transfer