Since Reynolds' seminal experiment in 1883, hydrodynamic stability has remained a central theme in fluid mechanics, particularly concerning the transition from laminar to turbulent flow. While eigenvalue analysis indicates that plane Couette flow and pipe Poiseuille flow remain linearly stable at all Reynolds numbers, experiments reveal that finite-amplitude perturbations can trigger turbulence at high Reynolds numbers—a phenomenon known as the subcritical transition. The physical mechanism of subcritical transition has been a longstanding problem in the field. In this talk, we present recent advances in understanding the transition mechanism through transition threshold problem.
