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There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon, however, is extremely difficult, requiring a new non-perturbative theory, such as statistical description. Furthermore, multi-scale interactions are responsible for inevitably complex dynamics in strongly non-equilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multi-scale interaction, a quasi-equilibrium state (the so-called self-organisation) can however be maintained. This special issue aims to present different theories of statistical mechanics to understand this challenging multiscale problem in turbulence. The 14 contributions to this Special issue focus on the various aspects of intermittency, coherent structures, self-organisation, bifurcation and nonlocality. Given the ubiquity of turbulence, the contributions cover a broad range of systems covering laboratory fluids (channel flow, the Von Kármán flow), plasmas (magnetic fusion), laser cavity, wind turbine, air flow around a high-speed train, solar wind and industrial application.

non-locality --- hybrid (U)RANS-LES --- channel flow --- thermodynamics --- Lévy noise --- non-local theory --- low speed streaks --- drop breakage --- pipe flow boundary layer --- bifurcation --- Langevin equation --- attached and separated flows --- anomalous diffusion --- kinetic theory --- stochastic processes --- self-organisation --- spatiotemporal chaos --- chaos --- bifurcations --- turbulent flow --- Lyapunov theory --- Rushton turbine --- turbulence --- intermittency --- information length --- denoise --- microcavity laser --- free vortex wake --- IDDES methodology --- local intermittency --- control strategy --- population balance equation --- Tsallis entropy --- coherent structures --- Fokker-Planck equation --- energy cascade --- fluid dynamics --- high efficiency impeller --- fractals --- large eddy simulation --- shear flows --- heat transport --- multifractal --- drop coalescence --- continuous wavelet transform --- T-junction --- scaling properties --- floating wind turbine --- scaling --- fractional Fokker–Plank equation --- magnetic confinement fusion --- multi-scale problem --- coherent structure --- solar wind --- trailing-edge flap --- turbulent transition --- turbulent boundary layer --- complex dynamics --- statistical mechanics