When is the onset of shear-flow turbulence discontinuous?
In plain words
Adding forces such as buoyancy, pipe curvature or magnetic fields to a pipe or channel flow can turn the gradual onset of turbulence into an abrupt jump with hysteresis, like boiling. No rule predicts which flows behave which way.
Precise statement
In wall-bounded shear flows with body forces (curved, heated or magnetohydrodynamic pipes and channels) or with suppressed large-scale flow, the turbulent fraction can jump discontinuously to zero, with metastable turbulence (Yang et al., Nature Physics 2026; Gome et al., PRL 2024, plane Couette flow). Find a criterion, in measurable quantities such as the kinetic-energy advection across laminar-turbulent interfaces or the fluctuation intensity in a one-field stochastic front model, that predicts whether the transition is continuous (directed percolation) or first order, and locate the tricritical point if one exists.
What would settle it
A parametric study in one flow family, such as a pipe with tunable body force, mapping the order of the transition against the proposed control parameter, including the tricritical point.
Status in the literature
Unverified note
The 2024 and 2026 works propose different controlling quantities (fluctuation intensity versus interfacial energy flux).