||The one-dimensional spectra in the streamwise direction of the velocity and vorticity fields in turbulent channel flows of Newtonian and non-Newtonian viscoelastic fluids are presented for friction Reynolds numbers up to Reτ0=1000Reτ0=1000.
The most striking feature induced by viscoelasticity is a marked drop, as rapid as k-5k-5, in the energy level of the streamwise velocity spectra at high wave-numbers, and in agreement with experimental data by Warholic et al. (Exps. Fluids., Vol. 27, pp. 461-472, 1999). The scaling of the streamwise velocity spectra for viscoelastic flow share some characteristics with the Newtonian spectra, but also exhibit unique properties. In particular, the logarithmic correction to the usual k-1k-1 law at the intermediate scales (eddies with size one to ten times the distance from the wall), found by del Álamo et al. (JFM Vol. 500, pp. 135-144, 2004) in the case of Newtonian turbulence, still holds in viscoelastic flows; although, with different scaling coefficients. In contrast, the longest modes of the spectra of the streamwise velocity component are found to behave differently. These modes are longer in viscoelastic flows and their scaling with the channel centerline velocity, here confirmed for Newtonian flow, fails for high drag reduction viscoelastic turbulent flows.
As for vorticity, it is found that the spectra of its cross-flow component in viscoelastic flows exhibit a significantly higher energy level at large scales, with a tendency towards a k-1k-1 law for high drag reduction and high Reynolds number.