  In this article, we show how to embed the so-called CH2 equations into the
geodesic flow of the Hdiv metric in 2D, which, itself, can be embedded in the
incompressible Euler equation of a non compact Riemannian manifold. The method
consists in embedding the incompressible Euler equation with a potential term
coming from classical mechanics into incompressible Euler of a manifold and
seeing the CH2 equation as a particular case of such fluid dynamic equation.
