Novel discoveries on the mathematical foundation of linear hydrodynamic stability theory

Y. Charles Li

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arXiv · 1711.00505

Novel discoveries on the mathematical foundation of linear hydrodynamic stability theory

Y. Charles Li

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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.

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Y. Charles Li. 2017-11-01. Novel discoveries on the mathematical foundation of linear hydrodynamic stability theory. https://arxiv.org/abs/1711.00505

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