We investigate three kinds of instabilities in binary immiscible homogeneous Bose-Einstein condensate, considering rubidium isotopes ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ confined in two-dimensional circular box. Rayleigh-Taylor and Kelvin-Helmholtz (KH) instability types are studied under strong perturbations. Without external perturbation, instabilities are also probed by immiscible-to-miscible quenching transition, under two different initial configurations. Our numerical simulations show that all such instability dynamics are dominated by large vortex production and sound-wave (phonon) propagation. For long-term propagation, vortex dynamics become dominant over sound waves in the KH instability, while sound-wave excitations predominate in the other cases. For all the dynamical simulations, the emergence of possible scaling laws are investigated for the compressible and incompressible parts of the kinetic energy spectra, in terms of the wave number $k$. The corresponding results are compared with the classical Kolmogorov scalings, $k^{-5/3}$ and $k^{-3}$, for turbulence, which are observed in the kinetic energy spectra at some specific time intervals.

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• Bose-Einstein condensates
• Cold atoms & matter waves
• Kelvin-Helmholtz instability
• Rayleigh-Taylor instability
• Vortex dynamics
• Nonlinear waves