The Onset of Intermittency in Stochastic Burgers Hydrodynamics

TL;DR

This paper investigates the emergence of intermittency in stochastic Burgers hydrodynamics by analyzing velocity gradient fluctuations through a field theoretical approach involving instantons and fluctuation effects, revealing renormalization effects on the dynamics.

Contribution

It introduces a systematic cumulant expansion to account for fluctuations around instantons, leading to a renormalized effective description of stochastic Burgers dynamics.

Findings

Fluctuations around instantons significantly influence the velocity gradient statistics.

Renormalization of the heat kernel propagator captures fluctuation effects.

The approach provides a practical framework for understanding intermittency in turbulence.

Abstract

We study the onset of intermittency in stochastic Burgers hydrodynamics, as characterized by the statistical behavior of negative velocity gradient fluctuations. The analysis is based on the response functional formalism, where specific velocity configurations - the viscous instantons - are assumed to play a dominant role in modeling the left tails of velocity gradient probability distribution functions. We find, as expected on general grounds, that the field theoretical approach becomes meaningful in practice only if the effects of fluctuations around instantons are taken into account. Working with a systematic cumulant expansion, it turns out that the integration of fluctuations yields, in leading perturbative order, to an effective description of the Burgers stochastic dynamics given by the renormalization of its associated heat kernel propagator and the external force-force correlation function.