Further analysis of the budgets of the dissipation tensor $\varepsilon_{ij}$ in turbulent plane channel flow

TL;DR

This paper extends previous DNS analysis of the dissipation tensor in turbulent channel flow, providing detailed insights into the mechanisms governing its transport and anisotropy, especially near the wall.

Contribution

It offers a detailed component-by-component analysis of the transport mechanisms of the dissipation tensor and compares them with Reynolds-stresses, highlighting differences in near-wall behavior.

Findings

Different near-wall behavior of pressure redistribution and diffusion terms.

The anisotropy of the destruction-of-dissipation tensor differs from that of Reynolds-stresses.

The dissipation tensor never reaches the 2-component state at the wall.

Abstract

Recent DNS results [Gerolymos G.A., Vallet I. : J. Fluid Mech. 807 (2016) 386--418] have provided data for the terms in the transport equations for the components of the dissipation tensor $\varepsilon_{ij}$ in low-Reynolds turbulent plane channel flow. The present paper extends the previous results by a detailed analysis of the behaviour of various mechanisms in the $\varepsilon_{ij}$-transport equations (production, diffusion, redistribution, destruction), with particular emphasis on the component-by-component comparison with the corresponding mechanisms in the transport equations for the Reynolds-stresses $r_{ij}$. The splitting of the pressure terms for the wall-normal components into redistribution and pressure-diffusion reveals substantially different behaviour near the wall. The wall-asymptotics of different terms in the transport equations are studied in detail, and examined using the DNS data. Both DNS data and wall-asympotic analysis show that the anisotropy of the destruction-of-dissipation tensor $\varepsilon_{\varepsilon_{ij}}$ is fundamentally different from that of $r_{ij}$ or $\varepsilon_{ij}$, never approaching the 2-component (2-C) state at the solid wall.