Self-sustaining and propagating mechanism of localized wave packet in plane-Poiseuille flow

Abstract

In this Letter, it is revealed that the convection velocity of a localized wave packet in two-dimensional plane-Poiseuille flow is determined by the solitary wave at the centerline of a vortex dipole, which is evinced by subtracting the base flow from the mean flow. The fluctuation component propagates obeying the local dispersion relation of the mean flow and oscillates with a global frequency selected by the upstream marginal absolute instability and, hence, is a traveling wave mode. The vortex dipole provides an unstable region for the fluctuation waves to grow up, and the Reynolds stress of the fluctuation waves leads to streaming components enhancing the vortex dipole. By applying localized initial disturbances, a nonzero wave-packet density is achieved at the threshold state, suggesting a first-order transition.