Turbulence in binary Bose-Einstein condensates generated by highly nonlinear Rayleigh-Taylor and Kelvin-Helmholtz instabilities

Quantum turbulence (QT) generated by the Rayleigh-Taylor instability in binary immiscible ultracold ⁸⁷Rb atoms at zero temperature is studied theoretically. We show that the quantum vortex tangle is qualitatively different from previously considered superfluids, which reveals deep relations between QT and classical turbulence. The present QT may be generated at arbitrarily small Mach numbers, which is a unique property not found in previously studied superfluids. By numerical solution of the coupled Gross-Pitaevskii equations we find that the Kolmogorov scaling law holds for the incompressible kinetic energy. We demonstrate that the phenomenon may be observed in the laboratory.