On the stochastic modeling of Lagrangian velocity and acceleration in turbulent flows

We propose to answer the following question: can we build up an infinitely differentiable stochastic process, such that asymptotically, when the Reynolds number goes to infinity, it becomes irregular (in a Holder sense) and intermittent (in a way we will clarify)? This has importance while modeling velocity and acceleration of particles following their trajectories in a turbulent flow. We propose such a process as a solution of a stochastic differential equation, making it causal. We proceed with analytical and numerical solutions, and compare against experimental and numerical data. Come, it will be fun.