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

TL;DR

This paper introduces a Monte Carlo method to numerically analyze the anomalous scaling of high-order velocity moments in the turbulent Burgers equation, providing a new approach for studying small-scale turbulence structures.

Contribution

The paper develops a Monte Carlo simulation framework based on the functional integral representation to study anomalous scaling in turbulence models.

Findings

Successfully determined anomalous scaling exponents for velocity differences.

Demonstrated the applicability of Monte Carlo methods to turbulence-related systems.

Provided a new numerical approach for analyzing small-scale turbulence phenomena.

Abstract

We present a new approach to determine numerically the statistical behavior of small-scale structures in hydrodynamic turbulence. Starting from the functional integral representation of the random-force-driven Burgers equation we show that Monte Carlo simulations allow us to determine the anomalous scaling of high-order moments of velocity differences. Given the general applicability of Monte Carlo methods, this opens up the possibility to address also other systems relevant to turbulence within this framework.