The formation of ion phase space vortexes in the ion two stream region behind electrostatic ion acoustic shocks are observed in a laboratory experiment. A detailed analysis demonstrates that the evolution of such vortexes is associated with ion-ion beam instabilities and a nonlinear equation for their initial evolution is derived. The results are supported by a numerical particle simulation. Also the possibility of vortex excitation by ion bursts and coalescence of two vortexes are demonstrated. The effects of finite ion temperature, particle trapping and charge exchange collisions are discussed and the results related to ionospheric observations.