Following recent experiments on ultracold dual superflows, we model in this work the dynamics of two harmonically trapped counterflowing superfluids. Using complementary analytical and numerical approaches, we study the shedding of elementary excitations triggered by the relative motion of the two species. We exhibit two different excitation mechanisms leading to distinct threshold velocities for the onset of dissipation: in addition to the parametric pair production present in homogeneous , galilean-invariant systems, we show that non-uniform motion and density inhomogeneities allow for a Landau-like decay mechanism where single excitations are produced.
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