Generalized 3D Kolmogorov flow: effect of weak large-scale damping

Turbulent flows can be understood as the superposition of a mean flow, which evolves slowly and is shaped by boundaries or forcing mechanisms, and a multitude of chaotic, short-lived fluctuations.
We performed pseudo-spectral simulations of a turbulent three-dimensional Kolmogorov flow with large-scale damping on an aspect-ratio-three domain, which is driven by a sinusoidal shearing body force. The visualization shows the vorticity averaged over the direction normal to the forcing plane to emphasize the large-scale counter-rotating vortices.
The bottom plot shows an effective wavenumber of the large-scale state --- 2/3 corresponds to two large-scale structures present in the flow, i.e. two pairs of counter-rotating vortices. Note that between t = 45T and t = 50T the large-scale state transitions between the k_s = 2/3 and the k_s = 1/3 states.
Please see arxiv.org/abs/2102.07675 for further details.