  We introduce a minimal model of energy transfer through scales to describe,
at a qualitative level, the subcritical transition between laminar and
turbulent flows, viewed in a statistical physics framework as a discontinuous
absorbing phase transition. The main control parameter of the model is a
Reynolds number that compares energy transfer to viscous dissipation on a large
length scale. In spite of its simplicity, the model qualitatively reproduces a
number of salient features of the subcritical laminar-turbulent transition,
including the existence of an absorbing laminar state, the discontinuous onset
of a metastable fluctuating turbulent state above a threshold Reynolds number,
and a faster-than-exponential increase of the turbulence lifetime when
increasing the Reynolds number. The behavior of the model is also consistent,
at high Reynolds number, with the Kolmogorov K41 phenomenology of fully
developed turbulence.
