On the Kutta-Joukowski Condition in Magnetohydrodynamics

The flow of an incompressible viscous fluid with electric conductivity past an insulated flat plate at a small incidence, in the presence of an aligned magnetic field, is studied. The solution for finite hydrodynamic and magnetic Reynolds numbers R , R m is uniquely determined by the linearized theory. Taking the limiting process: R =∞ and R m =∞, but ε = R m / R =finite, we obtain the flow of an inviscid fluid with infinite electric conductivity with a proper circulation. In the superalfvénic case the circulation coincides with that expected by the conventional Kutta-Joukowski condition, while in the subalfvénic case the circulation is given as a function of ε and the Alfvén number.