We study, by means of extensive direct numerical simulations, the turbulent flow produced by a two-dimensional cellular forcing in a cubic box with periodic boundary conditions. We find that, in spite of the developed turbulence that recovers isotropic features at small scales, the signature of forcing remains in the mean flow (averaged over time and over the homogeneous direction). This allows us to introduce a friction factor, whose dependence on the Reynolds number is investigated. We further show that the flow is characterized by large temporal fluctuations of the total energy, as a consequence of the exchange between the forced mean flow at large scales and turbulent fluctuations at small scales. Such temporal fluctuations produce a correction to the energy spectrum that can be explained by a simple dimensional argument.

• Received 19 November 2022
• Accepted 14 April 2023

DOI:https://doi.org/10.1103/PhysRevFluids.8.054601