Two-dimensional turbulence in a rectangular domain self-organises into
large-scale unidirectional jets. While several results are present to
characterize the mean jets velocity profile, much less is known about the
fluctuations. We study jets dynamics in the stochastically forced
two-dimensional Euler equations. In the limit where the average jets velocity
profile evolves slowly with respect to turbulent fluctuations, we employ a
multi-scale (kinetic theory) approach, which relates jet dynamics to the
statistics of Reynolds stresses. We study analytically the Gaussian
fluctuations of Reynolds stresses and predict the spatial structure of the jets
velocity covariance. Our results agree qualitatively well with direct numerical
simulations, clearly showing that the jets velocity profile are enhanced away
from the stationary points of the average velocity profile. A numerical test of
our predictions at quantitative level seems out of reach at the present day
