0 Extreme fluctuations and the finite lifetime of the turbulent state

The fundamental nature and stability of the turbulent state of fluids remains an open and challenging question. Fluid flow is characterized by a dimensionless number Re, which depends on the characteristic length L, velocity U and kinematic viscosity of the fluid ν through the relation Re ≡ UL/ν. As the Reynolds number increases from zero, the flow becomes increasingly structured and eventually statistical in nature, and at large Re, the flow is said to be turbulent[1]. The conventional assumption— that the turbulent state is absolutely stable—has been challenged recently by a series of theoretical[2] and experimental probes[3–7] of the transition to turbulence. Taken as a whole, these works suggest that turbulence might, in some flow regimes at least, be a long-lived metastable state[2, 8–11]. Such a view would be consistent with the fact that long-lived transient turbulent states can be excited as finite-amplitude instabilities of the laminar state, so that the laminar and turbulent states can coexist (for a review of foundational work in this area, see e.g. Ref. [12]; recent developments are summarized in Refs. [9–11, 13]). However, the question remains as to whether the turbulent state is ever sustainable with an infinite lifetime for finite Reynolds numbers. This is a difficult experimental question to decide, because the lifetime of the turbulent state can become so long that measurements become impossible. With the necessary restriction to a small range of Reynolds numbers, the data have, until recently, been difficult to interpret in a compelling way.