Scaling and Commonality in Anomalous Fluctuation Statistics in Models for Turbulence and Ferromagnetism

TL;DR

This paper analytically derives the probability distribution of energy fluctuations in turbulence and ferromagnetism models, revealing a shared functional form and a key control parameter linked to system scaling.

Contribution

It provides an analytical derivation of the fluctuation distribution from the scaling ansatz, connecting turbulence and ferromagnetic models through a common framework.

Findings

Derived the distribution's functional form analytically.

Identified the control parameter's dependence on system size and scaling exponents.

Suggested a possible generalization to other models.

Abstract

Recently, Portelli et al (2003) have semi-numerically obtained a functional form of the probability distribution of fluctuations in the total energy flow in a model for fluid turbulence. This follows earlier work suggesting that fluctuations in the total magnetization in the 2D X-Y model for a ferromagnet also follow this distribution. Here, starting from the scaling ansatz that is the basis of the turbulence model we analytically derive the functional form of this distribution and find its single control parameter that depends upon the scaling exponents and system size of the model. Our analysis allows us to identify this explicitly with that of the X-Y model, and suggest a possible generalization.