Statistical transition to turbulence in plane channel flow

Transition to turbulence in shear flows is characterized by intermittent laminar-turbulent patterns, which statistically proliferate or decay depending on the Reynolds number. The evolution of turbulent bands in plane channel flow is studied via direct numerical simulations in a narrow computational domain tilted with respect to the streamwise direction. Bands interact via their intervening quasi-laminar gap, impacting their propagation velocities. Turbulence decay and spreading processes are in most cases exponentially distributed, which is the signature of a memoryless process. Statistically estimated time scales for band decay or splitting depend super-exponentially on the Reynolds number and lead to the estimation of Reynolds number $Re_{\rm{cross}}\simeq 965$ above which splitting is more likely than decay. The associated time scales are over $10^6$ advection times. With such a low associated probability, the use of statistical mechanics methods such as a rare event algorithm is necessary to evaluate the mean decay or splitting time. Decay or splitting events are analyzed through the dynamics of large-scale Fourier components of the velocity, which statistically approaches a most-probable pathway.