Wave focusing and related multiple dispersion transitions in plane Poiseuille flows

• Published in: arXiv.org
• Main Authors: Fraternale, Federico, Nastro, Gabriele, Tordella, Daniela
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 08.03.2021
• Subjects: Asymptotic methods; Computer Science - Numerical Analysis; Fluid dynamics; Fluid flow; Laminar flow; Mathematics - Numerical Analysis; Perturbation; Physics - Fluid Dynamics; Reynolds number; Saddle points; Shear flow; Wave dispersion; Wave packets; Wavelengths
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2103.04650

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