Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization near $d=4$

TL;DR

This paper applies renormalization group and operator product expansion methods to analyze a tracer field advected by Navier-Stokes turbulence near four dimensions, revealing multifractal behavior in correlation functions.

Contribution

It introduces a one-loop renormalization analysis of a tracer field in compressible Navier-Stokes turbulence near four dimensions, highlighting multifractal properties.

Findings

Multifractal behavior of correlation functions established

Properties of equal-time structure functions analyzed

Leading one-loop approximation used for calculations

Abstract

The renormalization group approach and the operator product expansion technique are applied to the model of a tracer field advected by the Navier-Stokes velocity ensemble for a compressible fluid. The model is considered in the vicinity of the specific space dimension $d=4$. The properties of the equal-time structure functions are investigated. The multifractal behaviour of various correlation functions is established. All calculations are performed in the leading one-loop approximation.