Anomalous scaling in the random-force-driven Burgers equation: A Monte Carlo study

TL;DR

This paper introduces a Monte Carlo simulation approach to analyze anomalous scaling in the small-scale statistics of turbulence modeled by the Burgers equation, highlighting the method's broad applicability.

Contribution

It applies lattice Monte Carlo simulations to the Burgers equation, revealing anomalous scaling of velocity differences and demonstrating the method's potential for studying turbulent systems.

Findings

High-order moments exhibit anomalous scaling.

Monte Carlo methods are effective for turbulence analysis.

Framework applicable to other complex systems.

Abstract

We present a new approach to determine the small-scale statistical behavior of hydrodynamic turbulence by means of lattice simulations. Using the functional integral representation of the random-force-driven Burgers equation we show that high-order moments of velocity differences satisfy anomalous scaling. The general applicability of Monte Carlo methods provides the opportunity to study also other systems of interest within this framework.