Propagation mechanism of localized wave packet in plane-Poiseuille flow

TL;DR

This paper investigates how localized wave packets propagate in plane-Poiseuille flow, revealing the role of solitary waves, vortex dipoles, and the influence of flow instability on wave dynamics.

Contribution

It uncovers the propagation mechanism involving vortex dipoles and solitary waves, and links flow instability to wave packet behavior in plane-Poiseuille flow.

Findings

Convection velocity is determined by a solitary wave at the vortex dipole centerline.

Fluctuation oscillates with a global frequency set by upstream instability.

Wave-packet density indicates a first order transition at threshold.

Abstract

The convection velocity of localized wave packet in plane-Poiseuille flow is found to be determined by a solitary wave at the centerline of a downstream vortex dipole in its mean field after deducting the basic flow. The fluctuation component following the vortex dipole oscillates with a global frequency selected by the upstream marginal absolute instability, and propagates obeying the local dispersion relation of the mean flow. By applying localized initial disturbances, a nonzero wave-packet density is achieved at the threshold state, suggesting a first order transition.