Commun. Comput. Phys., 6 (2009), pp. 848-882.


On a Shallow Water Model for the Simulation of Turbidity Currents

T. Morales de Luna 1*, M. J. Castro Diaz 1, C. Pares Madronal 1, E. D. Fernandez Nieto 2

1 Analisis Matematico, Facultad de Ciencias - Univ. Malaga, Campus de Teatinos, 29071-Malaga, Spain.
2 Dpto. Matematica Aplicada I, ETS Arquitectura - Univ. Sevilla, Avda. Reina Mercedes N. 2, 41012-Sevilla, Spain.

Received 18 July 2008; Accepted (in revised version) 15 January 2009
Available online 12 March 2009

Abstract

We present a model for hyperpycnal plumes or turbidity currents that takes into account the interaction between the turbidity current and the bottom, considering deposition and erosion effects as well as solid transport of particles at the bed load due to the current. Water entrainment from the ambient water in which the turbidity current plunges is also considered. Motion of ambient water is neglected and the rigid lid assumption is considered. The model is obtained as a depth-average system of equations under the shallow water hypothesis describing the balance of fluid mass, sediment mass and mean flow. The character of the system is analyzed and numerical simulations are carried out using finite volume schemes and path-conservative Roe schemes.

AMS subject classifications: 74S10, 35L60, 35L65, 74G15

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Key words: Turbidity currents, hyperbolic systems, finite volume methods, path-conservative schemes, numerical modeling.

*Corresponding author.
Email: morales@anamat.cie.uma.es (T. Morales), castro@anamat.cie.uma.es (M. J. Castro), pares@anamat.cie.uma.es (C. Pares), edofer@us.es (E. D. Fernandez)
 

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