Critical velocity in a binary mixture of moving Bose condensates

We investigate the dynamic stability of two interacting Bose-Einstein condensates moving through each other with a relative velocity upsilon (r). We show that there exists a critical velocity upsilon ((c))(r) such that for upsilon>upsilon ((c))(r) the condensate mixture becomes unstable. We construct an analytic expression of the critical relative velocity and determine the unstable collective modes. We also discuss how; our results can be applied to matter-wave-mixing processes.