Lagrangian Statistics for Navier-Stokes Turbulence under Fourier-mode reduction: Fractal and Homogeneous Decimations

TL;DR

This paper investigates how Fourier-mode reduction affects small-scale turbulence in 3D flows, revealing decreased intermittency and vortex activity, while maintaining a fundamental Eulerian-Lagrangian connection.

Contribution

It introduces a study of Lagrangian turbulence under Fourier-mode reduction, highlighting the impact on high-frequency fluctuations and the persistence of a key dimensional relation.

Findings

High-frequency Lagrangian fluctuations decrease with mode decimation.

Intermittency reduces, leading to more Gaussian-like statistics.

Eulerian and Lagrangian statistics remain connected by a scale-invariant relation.

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.