Further analysis of the budgets of the dissipation tensor ${\epsilon }_{ij}$ 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 ${\epsilon }_{ij}$ 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 ${\epsilon }_{ij}$-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 ${\epsilon }_{{\epsilon }_{ij}}$ is fundamentally different from that of $r_{ij}$ or ${\epsilon }_{ij}$, never approaching the 2-component (2-C) state at the solid wall.

Initially this article was part of arXiv:1602.05022.v1, but to reduce length this content was removed from the final versions arXiv:1602.05022.v2 and arXiv:1602.05022.v3, with which there is no overlap

References in corpus (3)

• Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau }\approx 5200$
• The dissipation tensor ${\epsilon }_{ij}$ in wall turbulence
• Reynolds-stress model prediction of 3-D duct flows

Cited by in corpus (1)

• Algebraic proof and application of Lumley's realizability triangle