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 v_r. We show that there exists a critical velocity v^(c)_r such that for v_r>v^(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.