Abstract. Actuator disc theory is the basis for most rotor design methods, be it with many extensions and engineering rules added to make it a well-established method. However, the off-design condition of a very low rotational speed Ω of the disc is still a topic for scientific discussions. Several authors have presented solutions of the associated momentum theory for actuator discs with a constant circulation, the so-called Joukowsky discs, showing the efficiency Cp → ∞ for the tip speed ratio λ → 0. The momentum balance is very sensitive to the choice of the vortex core radius δ as the pressure and velocity gradients become infinite for δ → 0. Viscous vortex cores do not show this singular behaviour so an inviscid core model is sought which removes the momentum balance sensitivity to singular flow. A vortex core with a constant δ does so. Applying this in the momentum balance results in Cp → 0 for λ → 0, instead of Cp → ∞. At the disc the velocity in the meridian plane is shown to be constant. The Joukowsky actuator disc theory is confirmed by a very good match with the numerically obtained results. It gives higher Cp values than corresponding solutions for discs with a Goldstein-based wake circulation published in literature.