A deterministic cascade model to infer intermittency stochastics of Navier-Stokes

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Abstract. The ubiquity of the fundamental characteristic of turbulence, intermittency, is increasingly recognized in many fields. The multifractal analysis of various turbulence data, particularly from lab experiments and atmospheric sensed data, has rather constantly yielded a multifractality index of α ≈ 1.5 and a mean codimension of C1 ≈ 0.25, but with a given uncertainty. To reduce this uncertainty and understand the dynamical origin of these estimates, the multifractality of turbulence is investigated with the help of the deterministic Scaling Gyroscope Cascade (SGC) model. In this study, the forced SGC model is run with cascade levels of up to 14 and a duration of 2.5 × 104 large eddy turnover times. These simulations exhibit extreme spatial-temporal intermittency. Multifractal analysis confirms the empirical values α ≈ 1.5, C1 ≈ 0.25, showing almost independence on the forcing. It raises doubts about the Log-normal model, at least for hydrodynamic turbulence. In addition, the remaining uncertainty in multifractality resulting from the discrete numerical simulation method is investigated.

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