Recently the vortex method has been developed to simulate two dimensional incompressible separated flows at high Reynolds number. The motion of the vortex couple is studied in bounded and unbounded incompressible flow with the diffusion velocity method. The results show that little variation of viscous coefficient will change the motion of the vortex couple seriously. When the distance between the vortex couple is bigger than one certain distance, the viscous diffusion of the two vortices can be neglected. The diffusion velocity of the couple becomes bigger and dissipates. The Biot-Savart formulation of the compressible flow is deduced. The induced velocity of the vortices in the compressible flow is different from that in the incompressible flow due to the dilatation. The variation of the vorticity and the divergence of the velocity influence the vortices motion. When the divergence of the velocity is zero, the compressible Biot-Savart equation is degenerated to the incompressible Biot-Savart formulation. The revised Biot-Savart law of the compressible flow simulates the motion of the vortex couple in the unbounded flow. The motion of the vortex couple in the compressible flow is different from that in the incompressible flow. The vortex couple of the same direction moves outward along a circle that is not accurately a real circle. The vortex couple of the opposite direction moves inward or outward along with two parallel lines when the dilatation is negative or positive. The vortices will dissipate faster when the absolute magnitude of the dilatation is bigger.