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 three-dimensional flows under Fourier-mode reduction. The Navier–Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or homogeneous Fourier set. We find a strong sensitivity (reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree of mode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by a tendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales and frequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are still connected by a dimensional bridge-relation which is independent of the degree of Fourier-mode decimation.

Keywords

• isotropic and homogeneous turbulence
• multifractal theory
• Lagrangian dynamics
• intermittency
• 47.27.-i
• 82.20.-w