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

Abstract

Abstract. Recent DNS results [Gerolymos G.A., Vallet I. : J. Fluid Mech. 807 (2016) have provided data for the terms in the transport equations for the components of the dissipation tensor ε 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 ε 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 εε ij is fundamentally different from that of r ij or ε ij , never approaching the 2-component (2-C) state at the solid wall.

Componentality of velocity-derivatives in wall turbulence (and algebraic proof of Lumley's triangle)

“…The data are in excellent agreement (Gerolymos and Vallet 2016, figures 8-9) with those of Vreman and Kuerten (2014a) who studied the variances of the components of the velocity gradient (Vreman and Kuerten 2014b). Details on the numerical method (Gerolymos et al 2010) and on the computation of statistics were reported in previous work (Gerolymos and Vallet 2017).…”

“…represent the componentality of the small scales. Previous explorations of the componentality of various tensors in wall turbulence (Mansour et al 1988, Jovanović 2004, Gerolymos and Vallet 2016) have been particularly useful, not only regarding wall-asymptotic behaviour (Gerolymos and Vallet 2017), but also in clearly delimiting via AIM a strictly inner region (Krogstad and Torbergsen 2000) where outer scaling does not apply, i.e. the outer limit of the buffer zone ( ⪅ + y 80).…”