Reconstructing high-Reynolds-number flow statistics through a rescaling ensemble of Reynolds-similar flows

Direct numerical simulation (DNS) of turbulent flows requires resolving all relevant scales, imposing unfeasible computational requirements at large Reynolds numbers. In recent work (Bentkamp \& Wilczek, arXiv:2506.23712) a modeling approach based on an ensemble of lower-Reynolds-number flows with varying injection rates has been proposed. Here, we take this idea one step further: We present a method to replicate the velocity gradient statistics of high-Reynolds-number flows using only a single low-Reynolds-number DNS. We show that a statistical mixture, formed from an ensemble generated via Reynolds-similar rescaling, can accurately reconstruct the small-scale statistics of a reference simulation. We can construct a mixing distribution that reliably reproduces multiple observables, such as dissipation, enstrophy, and velocity gradient invariants using optimization approaches. Additionally, given a closed-form anomalous scaling exponent, we can infer the corresponding weight distribution for this superposition. This formalism also allows us to derive known relations between the anomalous scaling exponents, linking this method to the multifractal approach. A comparison to previous work suggests the potential for a generalized ensemble approach. These methods show promise for extrapolating high Reynolds number statistics at reduced computational cost.