  The decay of multicharged vortices in trapped Bose-Einstein condensates may
lead to a disordered vortex state consistent with the Vinen regime of
turbulence, characterized by an absence of large-scale flow and an
incompressible kinetic energy spectrum $E\propto k^{-1}$. In this work, we
study numerically the dynamics of a three-dimensional harmonically trapped
Bose-Einstein condensate excited to a Vinen regime of turbulence through the
decay of two doubly-charged vortices. First, we study the momentum distribution
and observe the emergence of a power-law behavior $n(k)\propto k^{-3}$
consistent with the coexistence of wave turbulence. We also study the kinetic
energy and particle fluxes, which allows us to identify a direct particle
cascade associated with the turbulent stage.
