Using a variety of classical geophysical flows dynamics, including the Surface Quasi-Geostrophy description  or the celebrated Lorenz-63 model , a stochastic framework has been implemented to help assess the role of unresolved motions on the large-scale flow dynamics. The proposed approach requires to re-evaluate the material derivative through a stochastic transport operator, derived from a reformulated material derivative. As a tes-bed example, a random version of the famous Lorenz system can thus be rigorously obtained to introduce and test small scale location uncertainties in large-scale representation of turbulence. The new system is compared to the usual eddy-viscosity assumption, pillar of most classical large eddy simulation. As demonstrated, the proposed framework offers means to very efficiently span the dynamical space, to explore in a much faster way the region of the deterministic attractor (figure 1).