Asymptotic Derivation of the Section-Averaged Shallow Water Equations for River Hydraulics.

Code:
17/2007
Title:
Asymptotic Derivation of the Section-Averaged Shallow Water Equations for River Hydraulics.
Date:
Friday 26th October 2007
Author(s):
Decoene, Astrid; Bonaventura, Luca; Miglio, Edie; Saleri, Fausto
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Abstract:
A section-averaged shallow water model for application to river hydraulics is derived asymptotically, starting from the three-dimensional Reynolds-averaged} Navier-Stokes equations for incompressible free surface flows. The resulting section-averaged equations take into account the effects of eddy viscosity, friction and of the three-dimensional geometry of the domain, up to the second order in the ratio between vertical and longitudinal scales. This novel derivation yields a friction term that is similar to that of the classical section-averaged shallow water model, but includes a correction that is dependent on the turbulent vertical viscosity model. Steady state analytic solutions for open channel flow have been computed for the derived model, obtaining solutions that are much closer to those of the three-dimensional model than the solutions computed by the classical one-dimensional shallow-water models.
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A. Decoene and L. Bonaventura and E. Miglio and F. Saleri, Asymptotic derivation of the section averaged shallow water equations for natural river hydraulics, Mathematical Models and Methods in Applied Sciences, Vol. 19, pp. 387-417, 2009