  We perform numerical simulations of vortex motion in a trapped Bose-Einstein
condensate by solving the two-dimensional Gross-Pitaevskii Equation in the
presence of a simple phenomenological model of interaction between the
condensate and the finite temperature thermal cloud. At zero temperature, the
trajectories of a single, off - centred vortex precessing in the condensate,
and of a vortex - antivortex pair orbiting within the trap, excite acoustic
emission. At finite temperatures the vortices move to the edge of the
condensate and vanish. By fitting the finite -temperature trajectories, we
relate the phenomenological damping parameter to the friction coefficients
$\alpha$ and $\alpha^{'}$, which are used to describe the interaction between
quantised vortices and the normal fluid in superfluid helium.
