Mean-Lagrangian formalism and covariance of fluid turbulence

TL;DR

This paper introduces a mean-field Lagrangian framework for fluid turbulence, enabling a covariant description of turbulence effects and extending classical correlation models within a unified, objective formalism.

Contribution

It develops a novel mean-field Lagrangian formalism for turbulence, providing a covariant approach and extending known correlation models.

Findings

Objective expression of turbulence visco-elastic effect

Extension of Lagrangian correlation in two-point closure

Unified covariant framework for turbulence modeling

Abstract

Mean-field-based Lagrangian framework is developed for the fluid turbulence theory. The space- time vector flow is naturally introduced from the mean velocity, which provides the Lagrangian picture based on the mean field in totally equivalent manner to that of the instantaneous field. The proposed framework is applied, on one hand, to one-point closure model, yielding an objective expression of the turbulence visco-elastic effect. Application to two-point closure, on the other hand, is also discussed, where natural extension of known Lagrangian correlation is discovered on the basis of extended covariance group.