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arXiv · 1803.03484

Spectral Stability of Inviscid Roll Waves

Mathew A. Johnson·Pascal Noble·L. Miguel Rodrigues·Zhao Yang·Kevin Zumbrun
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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.

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Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues, Zhao Yang, Kevin Zumbrun. 2018-03-09. Spectral Stability of Inviscid Roll Waves. https://doi.org/10.1007/s00220-018-3277-7

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