Nonlinearity of energy of Rankine flows on a torus

We study an ideal fluid flow on a torus described by the Weierstrass C-func tion. In spite of the analogy of this function to the Joukowski transformat ion on the plane the convex (planar) domain bounded by two streamlines pass ing through the stagnation points is not a disk. The energy of the flow out side the convex domain is generally nonlinear function of the strength of t he dipole; in fact the energy is in only two cases a linear function of the strength, and otherwise it is a quadratic function.