  We numerically study the dynamics of vortex lattice formation in a rotating
cigar-shaped Bose-Einstein condensate. The study is a three-dimensional
simulation of the Gross-Pitaevskii equation with a phenomenological dissipation
term. The simulations reveal previously unknown dynamical features of the
vortex nucleation process, in which the condensate undergoes a strongly
turbulent stage and the penetrating vortex lines vibrate rapidly. The
vibrations arise from spontaneous excitation of Kelvin waves on the
proto-vortices during a surface wave instability, caused by an inhomogeneity of
the condensate density along the elongated axial direction.
