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.

References in corpus (6)

• Multifractal statistics of Lagrangian velocity and acceleration in turbulence
• Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
• Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation
• Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence
• A new assessment of the second order moment of Lagrangian velocity increments in turbulence
• Introduction of longitudinal and transverse Lagrangian velocity increments in homogeneous and isotropic turbulence

Cited by in corpus (8)

• Multi-scale data reconstruction of turbulent rotating flows with Gappy POD, Extended POD and Generative Adversarial Networks
• From two-dimensional to three-dimensional turbulence through two-dimensional three-component flows
• Optimal tracking strategies in a turbulent flow
• The Onset of Thermalisation in Finite-Dimensional Equations of Hydrodynamics: Insights from the Burgers Equation
• Generative Adversarial Networks to infer velocity components in rotating turbulent flows
• On the thermalization of the three-dimensional, incompressible, Galerkin-truncated Euler equation
• Identifying the multifractal set on which energy dissipates in a turbulent Navier-Stokes fluid
• Onset of Intermittency and Multiscaling in Active Turbulence