  We study superfluidity of a cigar-shaped Bose-Einstein condensate (BEC) by
stirring it with a Gaussian potential oscillating back and forth along the
axial dimension of the condensate, motivated by experiments of C. Raman et al.
Phys. Rev. Lett. 83, 2502 (1999). Using classical-field simulations and
perturbation theory we examine the induced heating rate, based on the total
energy of the system, as a function of the stirring velocity $v$. We identify
the onset of dissipation by a sharply increasing heating rate above a velocity
$v_c$, which we define as the critical velocity. We show that $v_c$ is
influenced by the oscillating motion, the strength of the stirrer, the
temperature and the inhomogeneous density of the cloud. This results in a
vanishing $v_c$ for the parameters similar to the experiments, which is
inconsistent with the measurement of nonzero $v_c$. However, if the heating
rate is based on the thermal fraction after a 100 ms equilibration time, our
simulation recovers the experimental observations. We demonstrate that this
discrepancy is due to the slow relaxation of the stirred cloud and dipole mode
excitation of the cloud.
