A controllable vortex generator for reducing aerodynamic drag when vortex generation is not desired. The vortex generator includes a fin having a fixed forward portion and an aft portion which is movable between deflected and undeflected positions. At least a portion of the fin is formed of a memory shape alloy. The fin is attached to a base mountable to a surface such as the wing skin of an aircraft. An electrical resistance heating element is bonded to the fin and a controllable source of electric power is connected to the element. When the fin is heated by the element to a temperature equal to or greater than the transformation temperature of the alloy, the movable portion of the fin will move from a deflected position to an undeflected position, thereby reducing drag caused by the vortex generator.