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

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.