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On the stability of gradually varying mud-flows in open channels

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Abstract

In the present paper the stability of gradually varying mud-flows in wide open channel is analyzed. The governing equations derive from a Saint–Venant-like approach with a Herschel & Bulkley model for the fluid rheology. In order to define the stability of a given initial accelerating or decelerating flow depth profile, the spatial evolution of a wavefront is analyzed. A stability criterion based on the linearized flow model is introduced, showing that the streamwise non-uniformity of the flow substantially influences the stability limits. A positive flow depth slope induces a stabilization while a negative one determines a destabilizing effect. The dependency of the linear stability on the values of rheological parameters is deeply discussed. A non-linear analysis of the wavefront propagation, along with the full non-linear solution of the problem, has been carried out to confirm the role played by the initial profile on the flow stability. The results of the presented study may be useful for engineering applications in order to prevent or to inhibit roll-waves formation in subcritical flows of a Herschel & Bulkley fluid.

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Acknowledgments

The authors thank the reviewers for their valuable comments and suggestions, which substantially improved the paper quality.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Civile e Meccanica, Università di Cassino e del Lazio Meridionale, Via Di Biasio 43, 03043, Cassino, FR, Italy

    Cristiana Di Cristo

  2. Dipartimento di Ingegneria Civile, Design, Edilizia ed Ambiente, Seconda Università di Napoli, Via Roma 29, 81031, Aversa, CE, Italy

    Michele Iervolino & Andrea Vacca

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  1. Cristiana Di Cristo
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  2. Michele Iervolino
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Correspondence to Andrea Vacca.

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Di Cristo, C., Iervolino, M. & Vacca, A. On the stability of gradually varying mud-flows in open channels. Meccanica 50, 963–979 (2015). https://doi.org/10.1007/s11012-014-0075-y

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