Random vectorial fields representing the local structure of turbulence

Abstract

We propose a method to build up a random homogeneous, isotropic and incompressible turbulent velocity field that mimics turbulence in the inertial range. The underlying Gaussian field is given by a modified Biot-Savart law. The long range correlated nature of turbulence is then incorporated heuristically using a non linear transformation inspired by the recent fluid deformation imposed by the Euler equations. The resulting velocity field shows a non vanishing mean energy transfer towards the small scales and realistic alignment properties of vorticity with the eigenframe of the deformation rate.