Eulerian and Lagrangian statistics in Fourier-reduced Navier Stokes equations

Michele Buzzicotti

Hopeman 224

Turbulent flows are characterized by the presence of rare but strong fluctuations that dominate the statistical properties, making the turbulent velocity statistics highly non Gaussian. This phenomenon is called intermittency, and its origin is a central problem from both the theoretical and modeling points of view. Here, we present a numerical investigation of turbulent flows adopting a novel strategy which consists in changing the nonlinear interactions responsible of the energy transport across scales. The idea is to reduce the degrees of freedom of the flow, by keeping only a selection of Fourier modes belonging to a fractal set of dimension D. By tuning the fractal dimension D, we observe that strong fluctuations are suppressed and the system shows a quasi-singular transition from an intermittent to a Gaussian behaviour. We discuss results obtained for the one dimensional Burgers equation, often used as a model for compressible turbulent flows, together with those obtained for three dimensional incompressible, homogeneous and isotropic turbulence.