English

Novel discoveries on the mathematical foundation of linear hydrodynamic stability theory

Fluid Dynamics 2017-11-03 v1 Mathematical Physics Analysis of PDEs math.MP Chaotic Dynamics Atmospheric and Oceanic Physics

Abstract

We present some new discoveries on the mathematical foundation of linear hydrodynamic stability theory. The new discoveries are: 1. Linearized Euler equations fail to provide a linear approximation on inviscid hydrodynamic stability. 2. Eigenvalue instability predicted by high Reynolds number linearized Navier-Stokes equations cannot capture the dominant instability of super fast growth. 3. As equations for directional differentials, Rayleigh equation and Orr-Sommerfeld equation cannot capture the nature of the full differentials.

Keywords

Cite

@article{arxiv.1711.00505,
  title  = {Novel discoveries on the mathematical foundation of linear hydrodynamic stability theory},
  author = {Y. Charles Li},
  journal= {arXiv preprint arXiv:1711.00505},
  year   = {2017}
}