Monte Carlo simulations of the randomly forced Burgers equation

Abstract

The behaviour of the one--dimensional random--forced Burgers equation is investigated in the path integral formalism, using a discrete space--time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as structure functions, as ensemble averages over different field realizations. The regularization of shock solutions to the zero--viscosity limit (Hopf-eq.) eventually leads to constraints on lattice parameters, required for the stability of the simulations. Insight into the formation of localized structures (shocks) and their dynamics is obtained.

arXiv comment4 pages, 3 figures submitted to EPL

References in corpus (7)

• Turbulence without pressure
• Instantons in Burgers Equation
• Instantons and Intermittency
• Intermittency of Burgers' Turbulence
• Viscous Instanton for Burgers' Turbulence
• Effective action for stochastic partial differential equations
• Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids

Cited by in corpus (6)

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• 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
• Renormalization Group Analysis of Turbulent Hydrodynamics
• Monte Carlo approach to turbulence