  Most numerical models of binary stars - in particular neutron stars in
compact binaries - assume the companions to be either corotational or
irrotational. Either one of these assumptions leads to a significant
simplification in the hydrodynamic equations of stationary equilibrium. In this
paper we develop a new formalism for the construction of binary stars with
circulation intermediate between corotational and irrotational. Generalizing
the equations for irrotational flow we cast the Euler equation, which is an
algebraic equation in the case of corotational or irrotational fluid flow, as
an elliptic equation for a new auxiliary quantity. We also suggest a
parameterized decomposition of the fluid flow that allows for a variation of
the stellar circulation.
