  General conservation equations are derived for 2D dense granular flows from
the Euler equation within the Boussinesq approximation. In steady flows, the 2D
fields of granular temperature, vorticity and stream function are shown to be
encoded in two scalar functions only. We checked such prediction on steady
surface flows in a rotating drum simulated through the Non-Smooth Contact
Dynamics method. This result is non trivial because granular flows are
dissipative and therefore not necessarily compatible with Euler equation.
Finally, we briefly discuss some possible ways to predict theoretically these
two functions using statistical mechanics.
