Spatial correlations in turbulence: Predictions from the multifractal formalism and comparison with experiments

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Abstract
Questions about applicability of multiplicative cascade models for turbulent small‐scale intermittency (such as lognormal, random curdling, β, α, p models, etc.) are addressed by using the multifractal formalism to predict new properties of two‐point moments. These predictions are compared with experimental data. Measurements are performed in the wake of a cylinder and grid turbulence. Data at high Reynolds number in the atmospheric surface layer are also considered. The autocorrelation function of the local singularity strength α(x), as well as mixed moments of the form <εr(x)qεr(x+s)−q≳ are computed from the kinetic energy dissipation obtained from single‐component, single‐probe measurements using Taylor’s hypothesis. For flows at high‐enough Reynolds number, the α(x) autocorrelation function exhibits logarithmic decay with distance, as predicted from a random multiplicative cascade process. Some discrepancies exist in the quantitative details, implying enhanced randomization. The mixed moments are found to exhibit a scaling transition, also in agreement with the multiplicative models. The results illustrate the usefulness of the two‐point multifractal formalism in characterizing intermittency and, as far as two‐point statistics is concerned, lend further (qualified) support to the multiplicative cascade models.