  We introduce a stochastic version of Proudman-Taylor model, a 2D-3C fluid
approximation of the 3D Navier-Stokes equations, with the small-scale
turbulence modeled by a transport-stretching noise. For this model we may
rigorously take a scaling limit leading to a deterministic model with
additional viscosity on large scales. In certain choice of noises without
mirror symmetry, we identify an AKA effect. This is the first example with a 3D
structure and a stretching noise term.
