Transitions between large-scale flow states in turbulent 3D Kolmogorov flow

For most turbulent flows in nature, the idealization of statistical homogeneity and isotropy only applies to the small scales. The large scales are typically non-universal with pronounced inhomogeneities resulting from walls, large-scale driving etc. This motivates the investigation of the large-scale structure, turbulent fluctuations as well as their interaction in a canonical flow. Here we present results on a generalized turbulent Kolmogorov flow in three-dimensional periodic domains with aspect ratios larger than one. The flow is forced on a single Fourier mode and is subject to large-scale friction. The flow develops large-scale vortex patterns similar to two-dimensional Kolmogorov flow, even in the presence of intense three-dimensional small-scale fluctuations. We characterize transitions between different large-scale flow states as the large-scale friction is modified, including a regime reminiscent of noise-suppressed hysteresis. In addition to the large-scale flow features, we address the question of small-scale isotropy in the presence of large-scale anisotropies in this flow. Our results help to clarify the role of fluctuations for transitions in fully developed turbulence.