Multiscale Turbulence Models Based on Convected Fluid Microstructure

TL;DR

This paper develops multiscale turbulence models using the Euler-Poincaré framework and a kinematic sweeping ansatz, enabling better simulation of energy transfer across scales in turbulent flows.

Contribution

It introduces a novel multiscale turbulence modeling approach based on the Euler-Poincaré equations and KSA, extending existing models for improved nonlinear backscatter representation.

Findings

Derived multiscale equations suitable for turbulence modeling.

Extended known results to include nonlinear backscatter effects.

Proposed a framework for multiscale turbulence simulation.

Abstract

The Euler-Poincar\'e approach to complex fluids is used to derive multiscale equations for computationally modelling Euler flows as a basis for modelling turbulence. The model is based on a \emph{kinematic sweeping ansatz} (KSA) which assumes that the mean fluid flow serves as a Lagrangian frame of motion for the fluctuation dynamics. Thus, we regard the motion of a fluid parcel on the computationally resolvable length scales as a moving Lagrange coordinate for the fluctuating (zero-mean) motion of fluid parcels at the unresolved scales. Even in the simplest 2-scale version on which we concentrate here, the contributions of the fluctuating motion under the KSA to the mean motion yields a system of equations that extends known results and appears to be suitable for modelling nonlinear backscatter (energy transfer from smaller to larger scales) in turbulence using multiscale methods.