Theory and simulations of confined periodic turbulence

Abstract

Confined Periodic Turbulence (CPT) is numerical homogeneous turbulence with periodic conditions, over an extended time until the eddy size is only limited by the period L. With large or infinite Reynolds number, this allows a self-similar decaying state with a constant spectrum shape and turbulent kinetic energy k asymptotically equal to C CPT L 2 / t 2 where t is time and C CPT is a constant, as predicted by Skrbek & Stalp. This setting may provide a long inertial range for a given resolution and is free of inputs such as initial spectra or forcing devices. Outside the viscous range, it generates the same spectra as the Linear Forcing proposed by Lundgren and exercised by Rosales & Meneveau. We conduct DNS, with the viscosity artificially decreasing in time to keep the Reynolds number Re ≡ L k / ν approximately constant, and LES at infinite Reynolds number, with resolution 10243. The solutions indeed lose memory of initial conditions. Both agree well with Rosales & Meneveau and with the L 2 / t 2 conjecture although with modulations; C CPT is about 0.5. Kovasznay's extension of Kolmogorov's theory, based on the local energy-transfer rate across wavenumbers, predicts the spectrum well even for intermediate wavenumbers, with the Kolmogorov constant C K at 1.65.