We consider a family of processes obtained by decomposing the deterministic dynamics associated with some fluid models (e.g. Lorenz 96, 2d Galerkin-Navier-Stokes) into fundamental building blocks - i.e., minimal vector fields preserving some fundamental aspects of the original dynamics - and by sequentially following each vector field for a random amount of time. We characterize some ergodic properties of these stochastic dynamical systems and discuss their convergence to the original deterministic flow in the small noise regime. Finally, we show that the top Lyapunov exponent of these models is positive. This is joint work with Jonathan Mattingly and Omar Melikechi.