  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.
