You can double the number of effective poles by energizing adjacent coils in an overlapping fashion. That can reduce the number of coils to be wound and placed on the frame. The cost is an increase in the average current drawn by the coil assembly.

Is the rotating part to be magnetically polarized or simply attracted to a magnetic pole?

Does the rotating part (rotor) float unrestrained in the fluid, or is restrained by some other mechanism? If unrestrained, while the vortex be sufficient to keep the rotor centered in the steady state, and will the vortex form quickly enough to prevent the rotor from being attracted to and stuck to a pole?

Good Luck,

Bruce