  We investigate a procedure to generate turbulence in a trapped Bose-Einstein
condensate which takes advantage of the decay of multicharged vortices. We show
that the resulting singly-charged vortices twist around each other, intertwined
in the shape of helical Kelvin waves, which collide and undergo vortex
reconnections, creating a disordered vortex state. By examining the velocity
statistics, the energy spectrum, the correlation functions and the temporal
decay, and comparing these properties with the properties of ordinary
turbulence and observations in superfluid helium, we conclude that this
disordered vortex state can be identified with the `Vinen' regime of turbulence
which has been discovered in the context of superfluid helium.
