  We are concerned with a slow-fast system of coupled three dimensional
Navier--Stokes equations where the fast component is perturbed by an additive
Brownian noise. By means of the rough path theory we establish the convergence
in law of the slow component towards a Navier--Stokes system with an
It\^o--Stokes drift and a rough path driven transport noise. This gives an
alternative, more general and direct proof to Debussche, Pappalettera, 2022. In
particular, the limit driving rough path is identified as a geometric rough
path which does not necessarily coincide with the Stratonovich lift of the
Brownian motion.
