  The aim of the paper is to address the long time behavior of the Kuramoto
model of mean-field coupled phase rotators, subject to white noise and quenched
frequencies. We analyse the influence of the fluctuations of both thermal noise
and frequencies (seen as a disorder) on a large but finite population of $N$
rotators, in the case where the law of the disorder is symmetric. On a finite
time scale $[0, T]$, the system is known to be self-averaging: the empirical
measure of the system converges as $N\to \infty$ to the deterministic solution
of a nonlinear Fokker-Planck equation which exhibits a stable manifold of
synchronized stationary profiles for large interaction. On longer time scales,
competition between the finite-size effects of the noise and disorder makes the
system deviate from this mean-field behavior. In the main result of the paper
we show that on a time scale of order $ \sqrt{N}$ the fluctuations of the
disorder prevail over the fluctuations of the noise: we establish the existence
of disorder-induced traveling waves for the empirical measure along the
stationary manifold. This result is proved for fixed realizations of the
disorder and emphasis is put on the influence of the asymmetry of these
quenched frequencies on the direction and speed of rotation of the system.
Asymptotics on the drift are provided in the limit of small disorder.
