  In line with Pomeau's conjecture about the relevance of directed percolation
(DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal
stochastic model dedicated to the interpretation of the spatially intermittent
regimes observed in channel flow before its return to laminar flow. Numerical
simulations show that a regime with bands obliquely drifting in two stream-wise
symmetrical directions bifurcates into an asymmetrical regime, before
ultimately decaying to laminar flow. The model is expressed in terms of a
probabilistic cellular automaton evolving von Neumann neighbourhoods with
probabilities educed from a close examination of simulation results. It
implements band propagation and the two main local processes: longitudinal
splitting involving bands with the same orientation, and transversal splitting
giving birth to a daughter band with orientation opposite to that of its
mother. The ultimate decay stage observed to display one-dimensional DP
properties in a two-dimensional geometry is interpreted as resulting from the
irrelevance of lateral spreading in the single-orientation regime. The model
also reproduces the bifurcation restoring the symmetry upon variation of the
probability attached to transversal splitting, which opens the way to a study
of the critical properties of that bifurcation, in analogy with thermodynamic
phase transitions.
