Vortex shedding from an obstacle potential moving in a Bose-Einstein condensate is investigated. Long-lived alternately aligned vortex pairs are found to form in the wake, which is similar to the Bénard-von Kármán vortex street in classical viscous fluids. Various patterns of vortex shedding are systematically studied and the drag force on the obstacle is calculated. It is shown that the phenomenon can be observed in a trapped system.

The Rayleigh-Taylor instability at the interface in an immiscible two-component Bose-Einstein condensate is investigated using the mean field and Bogoliubov theories. Rayleigh-Taylor fingers are found to grow from the interface and mushroom patterns are formed. Quantized vortex rings and vortex lines are then generated around the mushrooms. The Rayleigh-Taylor instability and mushroom-pattern formation can be observed in a trapped system.

The dynamics of a phase-separated two-component Bose-Einstein condensate are investigated, in which a bubble of one component moves through the other component. Numerical simulations of the Gross-Pitaevskii equation reveal a variety of dynamics associated with the creation of quantized vortices. In two dimensions, a circular bubble deforms into an ellipse and splits into fragments with vortices, which undergo the Magnus effect. The Bénard-von Kármán vortex street is also generated. In three dimensions, a spherical bubble deforms into toruses with vortex rings. When two rings are formed, they exhibit leapfrogging dynamics.

The interfacial instability and subsequent dynamics in a phase-separated two-component Bose-Einstein condensate with rotational symmetry are studied. When the interatomic interaction or the trap frequency is changed, the Rayleigh-Taylor instability breaks the rotational symmetry of the interface, which is subsequently deformed into nonlinear patterns including mushroom shapes.

Capillary instability and the resulting dynamics in an immiscible two-component Bose-Einstein condensate are investigated using the mean-field and Bogoliubov analyses. A long, cylindrical condensate surrounded by the other component is dynamically unstable against breakup into droplets due to the interfacial tension arising from the quantum pressure and interactions. A heteronuclear system confined in a cigar-shaped trap is proposed for realizing this phenomenon experimentally.Comment: 7 pages, 6 figure