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 $C_{\mathrm{CPT}}{L}^2/t^2$ where t is time and $C_{\mathrm{CPT}}$ 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 $\mathrm{Re}\equiv L\sqrt{k}/\nu$ 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; $C_{\mathrm{CPT}}$ 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.

Keywords:

• Isotropic turbulence

Acknowledgments

This work was facilitated through the use of advanced computational, storage, and networking infrastructure provided by the HYAK supercomputer system at the University of Washington. The authors thank Dr A. Wray, Dr C. Mockett, and Prof. P. Davidson for their instructive comments.

Data availability statement

The time-series data used for the line graphs is available upon reasonable request. The three-dimensional flow field data used for Figures 1 and 2 is not available due to cessation of access to the HYAK storage system.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.