  Understanding the elementary mechanism for the dissipation of vortex energy
in quantum liquids is one central issue in quantum hydrodynamics, such as
quantum turbulence in systems ranging from neutron stars to atomic condensates.
In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature,
besides the vortex drift-out process from the boundary, vortex-antivortex pair
can annihilate in the bulk, but controversy remains on the number of vortices
involved in the annihilation process. We find there exists a dynamical
transition from four-body to three-body vortex annihilation processes with the
time evolution in a boundary-less uniform quasi-2D BEC. Such dynamical
transition depends on the initial vortex pair density, and occurs when the
sound waves generated in the vortex annihilation process surpass a critical
energy. With the confinement along the third direction is relaxed in a quasi-2D
BEC, the critical sound wave energy decreases due to the 3D vortex line curve
and reconnection, shifting the dynamical transition to the early time. Our work
reveals an elementary mechanism for the dissipation of vortex energy that may
help understand exotic matter and dynamics in quantum liquids.
