Wave focusing and related multiple dispersion transitions in plane Poiseuille flows

Motivated by the recent discovery of a dispersive-to-nondispersive transition for linear waves in shear flows, we accurately explored wavenumber-Reynolds number parameter map plane Poiseuille flow limit least-damped waves. We have discovered existence regions where dispersion and propagation features vary significantly from their surroundings. These are nested dispersive, low-wavenumber part map. This complex scenario demonstrates dispersive focusing wave envelopes evolving out an initial, spatially localized, three-dimensional perturbation. An asymptotic packet's representation, based on saddle-point method, allows to enlighten nature morphology, particular, arrow-shaped structure spatial spreading rates. A correlation is also highlighted between largest which most subject strong nonlinear coupling observations.