Journal of Applied Mathematics
Volume 2005 (2005), Issue 3, Pages 259-271
On the convective nature of roll waves instability
1Dipartimento di Ingegneria Idraulica ed Ambientale, Universitá di Napoli Federico II, Via Claudio 21, Napoli 80125, Italy
2Dipartimento di Ingegneria Civile, Seconda Universitá di Napoli, Via Roma 29, Aversa (Ce) 81031, Italy
Received 17 November 2004; Revised 25 January 2005
Copyright © 2005 C. Di Cristo and A. Vacca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 and
planes, where and 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.