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arXiv · 1912.07901

Derivation of an intermediate viscous Serre-Green-Naghdi equation

Denys Dutykh·Hervé Le Meur
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Abstract

In this note 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 linking the Reynolds number and the shallowness parameter. The computations presented in this note are performed in the fully nonlinear regime. The boundary layer flow reduces to a Prantdl-like equation. Further approximations seem to be needed to obtain a tractable model.

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Denys Dutykh, Hervé Le Meur. 2019-12-17. Derivation of an intermediate viscous Serre-Green-Naghdi equation. https://arxiv.org/abs/1912.07901

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