Wingtip Vortex: Heavy, Clean, Slow - Why?

You get the strongest wingtip vortices when an aircraft is flying heavy,
clean and slow. But why?

It has to do with the amount of lift being generated by the wing. HEAVY I
can understand. Heavier aircraft - you need more lift to keep it aloft.

But CLEAN? SLOW? Why do you get less vortex with the flaps down? Why does
a slow-moving aircraft generate a stronger vortex than a fast-moving
aircraft generating the same amount of lift? Is it because of the larger
angle of attack necessary to generate the same lift at a lower airspeed? If
so, why?

Eric