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The precise control over parameters such as the trapping frequencies and atomic interactions
renders Bose-Einstein condensates (BECs) one of the widely used nonlinear systems to study the turbulent
dynamics in quantum fluids, where the turbulence is referred to as quantum turbulence. In two-dimensional
quantum fluids, a topological excitation is a vortex with a quantized circulation around the vortex core with a
finite size. The multicomponent BEC setting, either of the same atomic species or of different atomic species,
significantly enriches the phenomenology of vortices due to the presence of two competing energy scales of
intra- and inter-component interactions. Depending on the strength of the intra- and inter-component
interactions, the system resides either in a miscible regime or in an immiscible one. We present turbulent
dynamics in two- component BECs modelled by the Gross-Pitaevskii equation. The turbulent dynamics is
induced via a stirring scheme that is commonly used in experiments. We considered both the symmetric and
asymmetric setup of the system parameters where the asymmetry is introduced through the difference of the
trap frequencies or that of the intra-component interaction strength. Since it is known that the trap geometry
plays a significant role in the vortex cluster formation, we implement the dynamics in a harmonic trap and
also in a steep-wall trap. We find that the initial turbulence generated via a stirring potential decays to the
interlaced vortex-antidark structures which, in turn, bear a large size of the vortex core. The corresponding
incompressible spectrum develops a k−3 power law for the wave numbers determined by the inverse of the
spin healing length, ξs and a flat region for the range of the wave number determined by the density healing
length, ξ , due to the bottleneck effect. This feature is enhanced for larger inter-component coupling strength.
In the case of the steep-wall trap, where formation of the Onsager cluster characterised by the large dipole
moment of the vortex charges is expected in a single-component BEC, the presence of the inter-component
coupling also causes the decay of vortices, preventing the persistence of the cluster configuration [1]. |