Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

摘要

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et?al.?(J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et?al.?(J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{st }$ the ratio between the eddy turnover time ( $q^{2}/unicode[STIX]{x1D716}$ , with $q^{2}$ being twice the turbulent kinetic energy and $unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ( $1/S$ ), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{st }$ , as well as $-langle Qangle =langle s_{ij}s_{ji}angle -langle unicode[STIX]{x1D714}_{i}unicode[STIX]{x1D714}_{i}/2angle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-langle Qangle pprox 0$ , that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulen