Discontinuous transition to shear flow turbulence

Abstract

Depending on the type of flow, the transition to turbulence can take one of two forms: either turbulence arises from a sequence of instabilities or from the spatial proliferation of transiently chaotic domains, a process analogous to directed percolation. The former scenario is commonly referred to as a supercritical transition and frequently encountered in flows destabilized by body forces, whereas the latter subcritical transition is common in shear flows. Both cases are inherently continuous in a sense that the transformation from ordered laminar to fully turbulent fluid motion is only accomplished gradually with flow speed. Here we show that these established transition types do not account for the more general setting of shear flows subject to body forces. The combination of the two continuous scenarios leads to the attenuation of spatial coupling; with increasing forcing amplitude, the transition becomes increasingly sharp and eventually discontinuous. We argue that the suppression of laminar–turbulent coexistence and the approach towards a discontinuous phase transition potentially apply to a broad range of situations including flows subject to, for example, buoyancy, centrifugal or electromagnetic forces.