Scaling law for a subcritical transition in plane Poiseuille flow

The scaling law for the threshold amplitude of perturbations to initiate a transition in subcritical plane Poiseuille flow as a function of the Reynolds number is demonstrated experimentally. The disturbances are introduced through an almost streamwise independent slot drilled at the bottom wall of a horizontal air-channel flow. Following the two stages of transition, linear transient growth and nonlinear secondary instability, it is found that the normalized critical injection rate (v0) scales with the Reynolds number (R) as v0 approximately R-3/2. This scaling law agrees with the theoretical predictions of Chapman J. Fluid Mech. 451, 34 (2002).].