Low-dimensional description of turbulent superstructures in three-dimensional Kolmogorov flow

Titelangaben

Álvarez-Garrido, Fabián ; Wilczek, Michael:
Low-dimensional description of turbulent superstructures in three-dimensional Kolmogorov flow.
In: Journal of Fluid Mechanics. Bd. 1039 (2026) . - A11.
ISSN 0022-1120
DOI: https://doi.org/10.1017/jfm.2026.11714

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Abstract

We investigate three-dimensional Kolmogorov flow as a model flow featuring turbulent superstructures, i.e. large-scale coherent structures within a turbulent flow. Previous works have shown that turbulent Kolmogorov flow features the emergence of various configurations of large-scale vortex pairs and dynamic switching between these flow states. Here, we devise a low-dimensional model and characterise the meandering of these large scales between different numbers of vortex pairs through two complex amplitudes. We identify these different large-scale states as remnants of instabilities far from the onset of turbulence. We obtain the statistics of the two complex amplitudes from direct numerical simulations. We then construct a set of stochastic amplitude equations whose statistical properties reproduce the ones observed in the three-dimensional Kolmogorov flow up to a fair agreement. Based on these results, we discuss how fast-evolving terms in the form of noise can be introduced into the averaged equations to capture the complex dynamics of the large scales. We thereby shed light on the interplay between the large scales and the small-scale fluctuations.