Spatio-temporal intermittency and phase transition in the subcritical transition of shear flows: Current status and open problems

<p indent="0mm">Transition to turbulence in shear flows has been a long-standing problem of fluid mechanics. In recent decades, great advancements have been made in this area, especially in the spatio-temporal intermittency of the subcritical transition. Even in simple shear flows, localized turbulence exhibits spatio-temporal complexity on large scales. Studies of this complexity have gradually revealed the relationship between the subcritical transition and non-equilibrium phase transition, i.e., transition probably belongs to the directed-percolation universality class that embraces a broad range of critical phenomenon. Although it has been long believed that the subcritical transition in all shear flows belongs to this universality class, only until very recently has the evidence been obtained in Taylor-Couette experiments. However, in pipe and channel flows, the vast spatial and temporal scales involved hinder experimental and numerical measurements to reach sufficiently close to the critical point. Besides, the spatio-temporal characteristics of localized turbulence in channel flow at low Reynolds numbers seem more complicated than the simple dynamics of directed percolation. Therefore, the generality of the phase-transition analogy of shear-flow transition remains to be clarified.