Local dissipation scales and energy dissipation-rate moments in channel flow

Abstract

Local dissipation-scale distributions and high-order statistics of the energy dissipation rate are examined in turbulent channel flow using very high-resolution direct numerical simulations at Reynolds numbers Re τ = 180, 381 and 590. For sufficiently large Re τ , the dissipation-scale distributions and energy dissipation moments in the channel bulk flow agree with those in homogeneous isotropic turbulence, including only a weak Reynolds-number dependence of both the finest and largest scales. Systematic, but Re τ -independent, variations in the distributions and moments arise as the wall is approached for y + 100. In the range 100 < y + < 200, there are substantial differences in the moments between the lowest and the two larger values of Re τ . This is most likely caused by coherent vortices from the near-wall region, which fill the whole channel for low Re τ .

On the universality of local dissipation scales in turbulent channel flow

“…When normalized by η 0 , this analytic result was found to be in good agreement with the PDFs calculated from the very high-resolution DNS data of three-dimensional homogeneous isotropic box turbulence of Schumacher (2007). The scale η 0 can be considered approximately analogous to η K (Hamlington et al 2012) and is found from (1.7). To do so, the approximation ζ 2n = 2an − 4bn 2 is utilized with a = 0.383 and b = 0.0166 (Yakhot 2006) …”

“…(1.10) Support for this dependence was found within the direct numerical simulation (DNS) results for box and channel flow turbulence (Schumacher 2007;Hamlington et al 2012) and its universality amongst different types of flow recently demonstrated by Schumacher et al (2014) through comparison of the Reynolds number dependence of the moments of ε produced within box, channel flow and Rayleigh-Bérnard convection.…”

“…This theory was tested by Schumacher (2007) using low-Reynolds-number DNS of homogeneous isotropic turbulence and again by Hamlington et al (2012) using DNS of turbulent channel flow. In both cases, good agreement was found with the theory.…”

“…Recently, Hamlington et al (2012) calculated the PDFs of η/η 0 from DNS results within turbulent channel flow and found that they exhibited strong wall-normal dependence, particularly near the wall. Similar location dependence of the PDF was also observed in free-shear flow by Morshed, Venayagamoorthy & Dasi (2013) who related this spatial dependence to the large-scale shear using a mean-shear Reynolds number.…”

A methodology to evaluate statistical errors in DNS data of plane channel flows

“…The main argument that support this approach is the convergence of statistics of higher order than the ones needed to compute the Reynolds stress tensor. These statistics are present in the dissipation and enstrophy budgets, which can be considered fingerprints of a turbulent flow (see Donzis et al [5] , Hamlington et al [9] , Jin et al [11] ).…”