Lagrangian statistics for Navier–Stokes turbulence under Fourier-mode reduction: fractal and homogeneous decimations

Abstract

We study small-scale and high-frequency turbulent fluctuations in\nthree-dimensional flows under Fourier-mode reduction. The Navier-Stokes\nequations are evolved on a restricted set of modes, obtained as a projection on\na fractal or homogeneous Fourier set. We find a strong sensitivity (reduction)\nof the high-frequency variability of the Lagrangian velocity fluctuations on\nthe degree of mode decimation, similarly to what is already reported for\nEulerian statistics. This is quantified by a tendency towards a quasi-Gaussian\nstatistics, i.e., to a reduction of intermittency, at all scales and\nfrequencies. This can be attributed to a strong depletion of vortex filaments\nand of the vortex stretching mechanism. Nevertheless, we found that Eulerian\nand Lagrangian ensembles are still connected by a dimensional bridge-relation\nwhich is independent of the degree of Fourier-mode decimation.\n