  We investigate excitations and fluctuations of Bose-Einstein condensates in a
two-dimensional torus with a uniformly moving Gaussian potential by solving the
Gross-Pitaevskii equation and the Bogoliubov equation. The energy gap $\Delta$
between the current-flowing metastable state (that reduces to the ground state
for sufficiently slowly-moving potential) and the first excited state vanishes
when the moving velocity $v$ of the potential approaches a critical velocity
v_c(>0). We find a scaling law $\Delta \propto (1-|v|/v_c)^{1/4}$, which
implies that a characteristic time scale diverges toward the critical velocity.
Near the critical velocity, we show that low-energy local density fluctuations
are enhanced. These behaviors can be regarded as precursor phenomena of the
vortex nucleation.
