Note on the stability of viscous roll waves

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• 作者：Blake Barker^a ; ¹ ; ^{Blake_Barker@brown.edu} ; Mathew A. Johnson^b ; ² ; ^{matjohn@ku.edu} ; Pascal Noble^c ; ^{pascal.noble@math.univ-toulouse.fr} ; Luis Miguel Rodrigues^d ; ³ ; ^{luis-miguel.rodrigues@univ-rennes1.fr} ; Kevin Zumbrun^e ; ⁴ ; ^{kzumbrun@indiana.edu}
• 关键词：Fluid mechanics ; Shallow water flows ; Roll waves
• 刊名：Comptes Rendus Mécanique
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：345
• 期：2
• 页码：125-129
• 全文大小：325 K
• 卷排序：345

文摘

In this note, we announce a complete classification of the stability of periodic roll-wave solutions of the viscous shallow water equations, from their onset at Froude number F≈2F≈2 up to the infinite Froude limit. For intermediate Froude numbers, we obtain numerically a particularly simple power-law relation between F   and the boundaries of the region of stable periods, which appears potentially useful in hydraulic engineering applications. In the asymptotic regime F→2F→2 (onset), we provide an analytic expression of the stability boundaries, whereas in the limit F→∞F→∞, we show that roll waves are always unstable.