Baropycnal Work: A Mechanism for Energy Transfer across Scales

Aarne Lees,Hussein Aluie

doi:10.3390/fluids4020092

Abstract

The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy budget after carrying out the appropriate scale decomposition. Strain generation by pressure and density gradients, both barotropic and baroclinic, also results from our analysis. These two processes underlie the recently identified mechanism of “baropycnal work”, which can transfer energy across scales in variable density flows. As such, baropycnal work is markedly distinct from pressure-dilatation into which the former is implicitly lumped in Large Eddy Simulations. We provide numerical evidence from 1024 3 direct numerical simulations of compressible turbulence. The data shows excellent pointwise agreement between baropycnal work and the nonlinear model we derive, supporting our interpretation of how it operates.

Highlights

Energy transfer across length scales is one of the defining characteristics of turbulent flows, the subject of which fits well under the “Multiscale Turbulent Transport” theme of this special issue in Fluids
Reference [15] argued that baropycnal work, Λ, is more similar in nature to deformation work, Π, in that it involves large-scales interacting with small-scales thereby allowing it to transfer energy across scales
The sharp spectral filter is not sign definite in x-space, which limits its utility in analyzing scale process in physical space

Summary

Introduction

Energy transfer across length scales is one of the defining characteristics of turbulent flows, the subject of which fits well under the “Multiscale Turbulent Transport” theme of this special issue in Fluids. In constant density canonical turbulence, the only pathway for transferring energy across scales is deformation work [1,2], which we represent below by Π. Reference [15] argued that baropycnal work, Λ, is more similar in nature to deformation work, Π, in that it involves large-scales interacting with small-scales thereby allowing it to transfer energy across scales. As such, it is fundamentally distinct from pressure dilatation which involves only large-scales and cannot transfer energy directly across scales

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Results

Conclusion