Experimental demonstration of scaling law for transition in subcritical channel flows

Scaling law for the threshold amplitude of perturbations to trigger nonlinearity in subcritical plane Poiseuille flow as function of the Reynolds number is demonstrated experimentally. The process is composed of a linear stage followed by a non linear one. The disturbances are introduced through an almost streamwise independent slot drilled at the bottom wall of a horizontal air channel flow. For low injection rates, long counter-rotating pair of vortices is observed undergoing transient growth, where as, above a critical injection rate of the disturbance, the pair of vortices undergo secondary instability leading to the nonlinear phenomenon of the initiation of hairpin vortices. The normalized critical injection rate ($v_0$) scales with the Reynolds number ($Re$) as $v_0 \sim Re^{-3/2}$, as predicted by Chapman [J. Fluid Mech. {\bf{451}}, 34 (2002)], using asymptotic theory. However, unlike in the theory which requires an impractical channel length of $O(R)$ for the growth of an infinitesimal small amplitude of vertical velocity ($v_0$) to $O (1)$ vertical vorticity, in the experiments a much shorter channel is used to obtain the same results by increasing the initial disturbance amplitude instead.