Lagrangian method for multiple correlations in passive scalar advection

TL;DR

This paper introduces a Lagrangian Monte Carlo method to compute multi-point correlations of a passive scalar in turbulent flows, especially effective as molecular diffusivity approaches zero, and applies it to the Kraichnan model.

Contribution

It presents a detailed Lagrangian approach for calculating n-point correlations in passive scalar advection, particularly useful for non-smooth velocity fields and the zero-diffusivity limit.

Findings

Accurate determination of anomalous intermittency corrections in the Kraichnan model.

Confirmation that anomalous corrections vanish as the velocity field's scaling exponent approaches 0 or 2.

Method is effective for studying passive scalar turbulence in various dimensions.

Abstract

A Lagrangian method is introduced for calculating simultaneous n-point correlations of a passive scalar advected by a random velocity field, with random forcing and finite molecular diffusivity kappa. The method, which is here presented in detail, is particularly well suited for studying the kappa tending to 0 limit when the velocity field is not smooth. Efficient Monte Carlo simulations based on this method are applied to the Kraichnan model of passive scalar and lead to accurate determinations of the anomalous intermittency corrections in the fourth-order structure function as a function of the scaling exponent xi of the velocity field in two and three dimensions. Anomalous corrections are found to vanish in the limits xi tending to 0 and xi tending to 2, as predicted by perturbation theory.