The minimal seeds (the disturbance with the lowest energy which triggers turbulence) for plane shear flows have been captured by the variational method dealing with the nonlinear Navier-Stokes equations. The subcritical transition of plane Poiseuille flow and the fluid structures of minimal seed are explored in the Reynolds number range 1500 ≤ Re ≤ 5000, the energy threshold of minimal seed scales Re-3 with respect to Re which agrees well with the theoretical prediction and the direct numerical simulations. The minimal seeds and the generated coherent structures corresponding to edge stage of plane Couette flow and plane Poiseuille flow are compared. The effect of base velocity and mean shear on minimal seed and subcritical transition is discussed.
The physical processes of subcritical transition of plane shear flows can be explained by minimal seeds. The naive and interesting question follows: If the generation of turbulence could be avoided or delayed by some flow control techniques? For example, the more nonlinear stable flow could be obtained if the energy threshold of minimal seed is increased by certain technique. The more nonlinear stable plane Poiseuille flow is achieved by the oscillating streamwise pressure gradient with proper pulsating frequency.