Breakdown of Kolmogorov scaling in models of cluster aggregation with deposition

TL;DR

This paper investigates the breakdown of Kolmogorov scaling in cluster aggregation models with deposition, revealing multifractal behavior through analytical and simulation methods, challenging classical turbulence theories.

Contribution

It demonstrates that correlation functions in the model exhibit multifractal scaling, contradicting Kolmogorov's linear scaling, supported by analytical and Monte Carlo simulation results.

Findings

Correlation functions show multifractal scaling.

Kolmogorov scaling is violated in the model.

Analytical results are confirmed by simulations.

Abstract

The steady state of the model of cluster aggregation with deposition is characterized by a constant flux of mass directed from small masses towards large masses. It can therefore be studied using phenomenological theories of turbulence, such as Kolmogorov's 1941 theory. On the other hand, the large scale behavior of the aggregation model in dimensions lower than or equal to two is governed by a perturbative fixed point of the renormalization group flow, which enables an analytic study of the scaling properties of correlation functions in the steady state. In this paper, we show that the correlation functions have multifractal scaling, which violates linear Kolmogorov scaling. The analytical results are verified by Monte Carlo simulations.