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30 June 2005 On the convective nature of roll waves instability
C. Di Cristo, A. Vacca
J. Appl. Math. 2005(3): 259-271 (30 June 2005). DOI: 10.1155/JAM.2005.259


A theoretical analysis of the Saint-Venant one-dimensional flow model is performed in order to define the nature of its instability. Following the Brigg criterion, the investigation is carried out by examining the branch points singularities of dispersion relation in the complex ω and k planes, where ω and k are the complex pulsation and wave number of the disturbance, respectively. The nature of the linearly unstable conditions of flow is shown to be of convective type, independently of the Froude number value. Starting from this result a linear spatial stability analysis of the one-dimensional flow model is performed, in terms of time asymptotic response to a pointwise time periodic disturbance. The study reveals an influence of the disturbance frequency on the perturbation spatial growth rate, which constitutes the theoretical foundation of semiempirical criteria commonly employed for predicting roll waves occurrence.


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C. Di Cristo. A. Vacca. "On the convective nature of roll waves instability." J. Appl. Math. 2005 (3) 259 - 271, 30 June 2005.


Published: 30 June 2005
First available in Project Euclid: 25 July 2005

zbMATH: 1092.76028
MathSciNet: MR2201974
Digital Object Identifier: 10.1155/JAM.2005.259

Rights: Copyright © 2005 Hindawi

Vol.2005 • No. 3 • 30 June 2005
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