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

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.

11 pages, 3 figures; v2: references updated, added some clarifying comments on the applicability of Monte Carlo simulations and an outlook on issues expected to arise for the case of Navier-Stokes turbulence

References in corpus (8)

• Burgers Turbulence
• Intermittency and Universality in Fully-Developed Inviscid and Weakly-Compressible Turbulent Flows
• Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?
• Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids
• Effects of forcing in three dimensional turbulent flows
• Gauge fixing, BRS invariance and Ward identities for randomly stirred flows
• Monte Carlo simulations of the randomly forced Burgers equation
• Anomalous scaling in the random-force-driven Burgers equation: A Monte Carlo study

Cited by in corpus (5)

• The instanton method and its numerical implementation in fluid mechanics
• Introduction to the nonequilibrium functional renormalization group
• Numerical study of extreme mechanical force exerted by a turbulent flow on a bluff body by direct and rare-event sampling techniques
• A Hybrid Monte Carlo algorithm for sampling rare events in space-time histories of stochastic fields
• Anomalous scaling in the random-force-driven Burgers equation: A Monte Carlo study