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Asymptotic derivation of the section-averaged shallow water equations for natural river hydraulics. (English) Zbl 1207.35092
Under some general assumptions on the geometry of the channel, the authors derive the section-averaged shallow water model for river and open channel hydraulics by asymptotic analysis from the three dimensional Reynolds-averaged Navier-Stokes equations for incompressible free surface flows. Especially, in their derivation a generalized friction term is obtained. This friction term can be computed directly from three dimensional turbulent models without local uniformity assumption. Moreover, the authors’ analysis show that their obtained friction term justifies a posteriori these empirical closures, then can avoid the assumptions on local flow uniformity on which these closures rely.
Reviewer: Cheng He (Beijing)

MSC:
35C20 Asymptotic expansions of solutions to PDEs
35L60 First-order nonlinear hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
65Z05 Applications to the sciences
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