The three-dimensional turbulent cellular flow

TL;DR

This study uses direct numerical simulations to analyze a three-dimensional turbulent flow driven by two-dimensional cellular forcing, revealing near-isotropic small-scale turbulence despite anisotropic forcing and highlighting energy exchange dynamics.

Contribution

It provides new insights into turbulence recovery and energy exchange mechanisms in cellular flows with anisotropic forcing.

Findings

Turbulence becomes nearly isotropic at small scales.

The flow exhibits large temporal energy fluctuations.

A correction to the energy spectrum is explained by dimensional analysis.

Abstract

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. In spite of the strong anisotropy of the forcing, we find that turbulence recovers almost complete isotropy at small scales. Nonetheless, the signature of the forcing remains in the mean flow (averaged over time and over the homogeneous direction) and this allows to introduce a friction factor, whose dependence on the Reynolds number is investigated. We further find 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.