On the Vortex Dynamics in Fractal Fourier Turbulence

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.

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Cited by in corpus (10)

• Cascades and transitions in turbulent flows
• Dual constant-flux energy cascades to both large scales and small scales
• Lagrangian Statistics for Navier-Stokes Turbulence under Fourier-mode reduction: Fractal and Homogeneous Decimations
• Suppressing thermalization and constructing weak solutions in truncated inviscid equations of hydrodynamics: Lessons from the Burgers equation
• Flow structures govern particle collisions in turbulence
• The Onset of Thermalisation in Finite-Dimensional Equations of Hydrodynamics: Insights from the Burgers Equation
• On the thermalization of the three-dimensional, incompressible, Galerkin-truncated Euler equation
• Intermittency, cascades and thin sets in three-dimensional Navier-Stokes turbulence
• The statistical properties of turbulence in the presence of a smart small-scale control
• Revisiting the SABRA Model: Statics and Dynamics