  The transitional and well-developed regimes of turbulent shear flows exhibit
a variety of remarkable scaling laws that are only now beginning to be
systematically studied and understood. In the first part of this article, we
summarize recent progress in understanding the friction factor of turbulent
flows in rough pipes and quasi-two-dimensional soap films, showing how the data
obey a two-parameter scaling law known as roughness-induced criticality, and
exhibit power-law scaling of friction factor with Reynolds number that depends
on the precise form of the nature of the turbulent cascade. These results hint
at a non-equilibrium fluctuation-dissipation relation that applies to turbulent
flows. The second part of this article concerns the lifetime statistics in
smooth pipes around the transition, showing how the remarkable
super-exponential scaling with Reynolds number reflects deep connections
between large deviation theory, extreme value statistics, directed percolation
and the onset of coexistence in predator-prey ecosystems. Both these phenomena
reflect the way in which turbulence can be fruitfully approached as a problem
in non-equilibrium statistical mechanics.
