On the convective nature of roll waves instability
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, w...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/JAM.2005.259 |
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| Summary: | 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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| ISSN: | 1110-757X 1687-0042 |