Title: 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.