Kolmogorov Dispersion for Turbulence in Porous Media: A Conjecture

TL;DR

This paper proposes a theoretical approach linking self-avoiding walk statistics and fractal geometries to estimate the Kolmogorov energy dispersion exponent in turbulence within porous media, suggesting it is less than the classical 5/3 value.

Contribution

It introduces a novel conjecture connecting SAW mapping, fractal geometries, and turbulence in porous media to estimate the dispersion exponent.

Findings

Estimated Kolmogorov exponent less than 5/3 for porous media turbulence

Link between polymer size exponents and turbulence dispersion

Theoretical framework for turbulence in disordered fractal structures

Abstract

We will utilise the self-avoiding walk (SAW) mapping of the vortex line conformations in turbulence to get the Kolmogorov scale dependence of energy dispersion from SAW statistics, and the knowledge of the disordered fractal geometries on the SAW statistics. These will give us the Kolmogorov energy dispersion exponent value for turbulence in porous media in terms of the size exponent for polymers in the same. We argue that the exponent value will be somewhat less than 5/3 for turbulence in porous media.