Electromagnetic flow control leading to a strong drag reduction of a sphere

We consider the flow of an electrically conducting fluid around a sphere with some internal source of alternating magnetic field. The resulting electromagnetic forces of this inductive scheme lead to a thrust of the sphere and a changed drag coefficient which balance each other in the self-moved regime. Allowing for a free choice of physically meaningful field distributions, the inverse problem is addressed of looking for such magnetic fields which result in a low drag. A gradient-type optimization is applied in the Stokes limit, and the same electromagnetic force fields are then applied at higher Reynolds numbers. Without claiming to have found a global optimum, we present some examples of electromagnetic forces providing strong reductions of the sphere drag by factors of 103...104 compared to the non-magnetic case. Numerical results up to Re=1000 are given, the corresponding modifications of surface pressure and vorticity are discussed.