Tollmien-Schlichting waves in the subsonic regime
Abstract
The Tollmien-Schlichting (T-S) waves play a key role in the early stages of boundary layer transition. In a breakthrough work, Grenier, Guo and Nguyen gave the first rigorous construction of the T-S waves of temporal mode for the incompressible fluid. Yang and Zhang recently made an important contribution by constructing the compressible T-S waves of temporal mode for certain boundary layer profiles with Mach number . In this paper, we construct the T-S waves of both temporal mode and spatial mode to the linearized compressible Navier-Stokes system around the boundary layer flow in the whole subsonic regime , including the Blasius profile. Our approach is based on a novel iteration scheme between the quasi-incompressible and quasi-compressible systems, with a key ingredient being the solution of an Orr-Sommerfeld type equation using a new Airy-Airy-Rayleigh iteration instead of Rayleigh-Airy iteration introduced by Grenier, Guo and Nguyen. We believe the method developed in this work can be applied in solving other related problems for subsonic flows.
Keywords
Cite
@article{arxiv.2305.03229,
title = {Tollmien-Schlichting waves in the subsonic regime},
author = {Nader Masmoudi and Yuxi Wang and Di Wu and Zhifei Zhang},
journal= {arXiv preprint arXiv:2305.03229},
year = {2023}
}