HYDRODYNAMICAL TURBULENCE BY FRACTAL FOURIER DECIMATION

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We present a systematic numerical investigation of high-resolution 3D isotropic and homogeneous turbulence resolved on a decimated set of Fourier modes. Fractal decimation acts to decrease the effective dimensionality of the flow by allowing triadic interactions only in a set of Fourier modes N(k) proportional to k^DF for large k. While keeping the symmetries of the original 3D Navier-Stokes equations unchanged, a dramatic change in small-scale statistics is detected at decreasing the fractal dimension DF . Already at fractal dimension DF = 2.8, a global self-similar behaviour is observed in the inertial range of scales, the consequence of such transition are the restoration of the scaling symmetry and vorticity distribution that becomes close to Gaussian. We relate the results to the different roles of local vs non-local interactions in the energy transfer range.