One of the theoretical challenges in the study of turbulence is to develop an effective, coarse-grained model of its behaviour on a macroscopic scale. Turbulent flows are out-of-equilibrium systems that exhibit stochastic behaviour due to small-scale perturbations affecting macroscopic dynamics within a finite amount of time. This property, known as the spontaneous stochasticity of the incompressible Navier–Stokes equation, challenges traditional coarse-graining approaches because unresolved scales cannot simply be neglected. In this work, these scales are modelled as vanishing, momentum-conserving, multiplicative noise. The resulting stochastic Navier–Stokes equation is analysed using Macroscopic Fluctuation Theory (MFT), a statistical framework for non-equilibrium systems governed by stochastic hydrodynamics.