On the Vortex Dynamics in Fractal Fourier Turbulence

TL;DR

This paper investigates how fractal Fourier mode reduction affects turbulence dynamics, revealing that decreasing the fractal dimension diminishes vortex stretching and leads to Gaussian velocity statistics, indicating suppression of turbulence intermittency.

Contribution

It introduces a novel approach of fractal Fourier decimation to study turbulence, showing how mode reduction impacts vortex stretching and statistical properties.

Findings

Reducing fractal dimension weakens vortex stretching.

Mode reduction leads to Gaussian velocity statistics.

Turbulence intermittency is suppressed with fractal mode decimation.

Abstract

Incompressible, homogeneous and isotropic turbulence is studied by solving the Navier-Stokes equations on a reduced set of Fourier modes, belonging to a fractal set of dimension $D$. By tuning the fractal dimension parameter, we study the dynamical effects of Fourier decimation on the vortex stretching mechanism and on the statistics of the velocity and the velocity gradient tensor. In particular, we show that as we move from $D=3$ to $D \sim 2.8$, the statistics gradually turns into a purely Gaussian one. This result suggests that even a mild fractal mode reduction strongly depletes the stretching properties of the non-linear term of the Navier-Stokes equations and suppresses anomalous fluctuations.