  The 2D Euler equations are a simple but rich set of non-linear PDEs that
describe the evolution of an ideal inviscid fluid, for which one dimension is
negligible. Solving numerically these equations can be extremely demanding.
Several techniques to obtain fast and accurate simulations have been developed
during the last decades. In this paper, we present a novel approach which
combines recent developments in the stochastic model reduction and conservative
semi-discretization of the Euler equations. In particular, starting from the
Zeitlin model on the 2-sphere, we derive reduced dynamics for large scales and
we close the equations either deterministically or with a suitable stochastic
term. Numerical experiments show that, after an initial turbulent regime, the
influence of small scales to large scales is negligible, even though a non-zero
transfer of energy among different modes is present.

Numerical Analysis;Numerical Analysis