On the hyperbolic nature of the equations of alluvial river hydraulics and the equivalence of stable and energy dissipating shocks |
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| Authors: | D D L Zanraea D J Needham |
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| Institution: | School of Mathematics, University of East Anglia , Norwich, NR4 7TJ, U.K |
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| Abstract: | Abstract The depth-averaged hydraulic equations augmented with a suitable bed-load sediment transport function form a closed system which governs the one-dimensional flow in an alluvial river or channel. In this paper, it is shown that this system is hyperbolic and yields three families of shock-wave solutions. These are determined to be temporally stable in restricted regions of the (H, F 0)-plane, via the Lax shock inequalities. Further, it is demonstrated that this criterion is equivalent to the energy dissipation criterion developed by Needham and Hey (1991). |
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| Keywords: | Magma numerical modeling volcano multiphase flow |
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