Spectral stability of inviscid roll-waves

Abstract : We carry out a systematic analytical and numerical study of spectral stability of dis-continuous roll wave solutions of the inviscid Saint Venant equations, based on a periodic Evans-Lopatinsky 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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Contributeur : Pascal Noble <>
Soumis le : dimanche 9 septembre 2018 - 11:05:51
Dernière modification le : jeudi 27 septembre 2018 - 01:20:10

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  • HAL Id : hal-01870739, version 1

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Mathew Johnson, Pascal Noble, L Rodrigues, Zhao Yang, Kevin Zumbrun. Spectral stability of inviscid roll-waves. 2018. 〈hal-01870739〉

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