Spectral Stability of Inviscid Roll Waves
Analysis of PDEs
2018-11-14 v1 Fluid Dynamics
Abstract
We carry out a systematic analytical and numerical study of spectral stability of discontinuous roll wave solutions of the inviscid Saint Venant equations, based on a periodic Evans-Lopatinski determinant analogous to the periodic Evans function of Gardner in the (smooth) viscous case, obtaining a complete spectral stability diagram useful in hydraulic engineering and related applications. In particular, we obtain an explicit low-frequency stability boundary, which, moreover, matches closely with its (numerically-determined) counterpart in the viscous case. This is seen to be related to but not implied by the associated formal first-order Whitham modulation equations.
Keywords
Cite
@article{arxiv.1803.03484,
title = {Spectral Stability of Inviscid Roll Waves},
author = {Mathew A. Johnson and Pascal Noble and L. Miguel Rodrigues and Zhao Yang and Kevin Zumbrun},
journal= {arXiv preprint arXiv:1803.03484},
year = {2018}
}
Comments
45 pages, 11 figures