  We are interested in asymptotic models for the propagation of internal waves
at the interface between two shallow layers of immiscible fluid, under the
rigid-lid assumption. We review and complete existing works in the literature,
in order to offer a unified and comprehensive exposition. Anterior models such
as the shallow water and Boussinesq systems, as well as unidirectional models
of Camassa-Holm type, are shown to descend from a broad Green-Naghdi model,
that we introduce and justify in the sense of consistency. Contrarily to
earlier works, our Green-Naghdi model allows a non-flat topography, and
horizontal dimension d = 2. Its derivation follows directly from classical
results concerning the one-layer case, and we believe such strategy may be used
to construct interesting models in different regimes than the
shallow-water/shallow-water studied in the present work.
