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.

Comments: 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