Predicting any small-scale statistics of high-Reynolds-number turbulence using ensemble simulations

The complex small-scale statistics of turbulence are a result of the combined cascading dynamics through all scales of the flow. Predicting these statistics using fully resolved simulations at the high Reynolds numbers that typically occur in many real-world flows will exceed the capabilities of even the largest supercomputers for the foreseeable future. We here propose a joint theoretical and computational framework that leverages the common observation that high-Reynolds-number flows are organized in clusters of intense turbulent activity separated by large regions of quiescent flow. Our core assumption is an ensemble hypothesis, stating that the statistical properties of the small scales can be emulated by the mixture of a heterogeneous ensemble of lower-Reynolds-number simulations. By connecting this approach to anomalous scaling exponents, we enable accurate high-Reynolds-number extrapolation of arbitrary small-scale statistics. We evaluate the performance of our hybrid method at the example of various velocity gradient statistics from our own simulations and recent literature.