  In the present paper we study slow-fast systems of coupled equations from
fluid dynamics, where the fast component is perturbed by additive noise. We
prove that, under a suitable limit of infinite separation of scales, the slow
component of the system converges in law to a solution of the initial equation
perturbed with transport noise, and subject to the influence of an additional
It\=o-Stokes drift. The obtained limit equation is very similar to turbulent
models derived heuristically. Our results apply to the Navier-Stokes equations
in dimension $d=2,3$; the Surface Quasi-Geostrophic equations in dimension
$d=2$; and the Primitive equations in dimension $d=2,3$.
