Derivation of a Viscous Serre–Green–Naghdi Equation: An Impasse?
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In this article, we present the current status of the derivation of a viscous Serre–Green–Naghdi system. For this goal, the flow domain is separated into two regions. The upper region is governed by inviscid Euler equations, while the bottom region (the so-called boundary layer) is described by Navier–Stokes equations. We consider a particular regime binding the Reynolds number and the shallowness parameter. The computations presented in this article are performed in the fully nonlinear regime. The boundary layer flow reduces to a Prandtl-like equation that we claim to be irreducible. Further approximations are necessary to obtain a tractable model.
2008 ◽
Vol 614
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pp. 315-327
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2013 ◽
Vol 14
(6)
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pp. 2091-2104
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1974 ◽
Vol 62
(2)
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pp. 289-304
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