Instantons and Fluctuations in a Lagrangian Model of Turbulence

TL;DR

This paper analytically investigates the RFD model for turbulence intermittency using the MSRJD formalism, focusing on instanton solutions and fluctuation effects on velocity gradient PDFs.

Contribution

It introduces a hierarchical perturbative analysis of fluctuations around instantons in the RFD model, improving understanding of non-Gaussian features in turbulence.

Findings

Subleading corrections refine the non-Gaussian core of vgPDFs.

Instanton solutions capture the main shape of velocity gradient distributions.

Renormalized effective actions incorporate fluctuation effects effectively.

Abstract

We perform a detailed analytical study of the Recent Fluid Deformation (RFD) model for the onset of Lagrangian intermittency, within the context of the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) path integral formalism. The model is based, as a key point, upon local closures for the pressure Hessian and the viscous dissipation terms in the stochastic dynamical equations for the velocity gradient tensor. We carry out a power counting hierarchical classification of the several perturbative contributions associated to fluctuations around the instanton-evaluated MSRJD action, along the lines of the cumulant expansion. The most relevant Feynman diagrams are then integrated out into the renormalized effective action, for the computation of velocity gradient probability distribution functions (vgPDFs). While the subleading perturbative corrections do not affect the global shape of the vgPDFs in an appreciable qualitative way, it turns out that they have a significant role in the accurate description of their non-Gaussian cores.