The vortex induced reconnection(VIR) processes in periodic current sheet systems with shear flows at near and supper Alfvén speed are investigated by using the two dimensional compressible magnetohydrodynamics(MHD) simulation method. The results show that, the VIR processes in the neignbouring current sheets can interact with each other, and their linear growth rate is enhanced and decreased for the cases of antisymmetric and symmetric modes, respectively.