Multimedialne seminarium z ekono- i socjofizyki

We present a fractal sub-grid scale model for large eddy simulation (LES) of atmospheric flow. The fractal model is based on the fractality assumption of turbulent velocity field with a dynamical hypothesis based on energy dissipation. The fractal model reconstruct sub-grid velocity field from the knowledge of its filtered values on LES grid, by means of fractal interpolation, proposed by Scotti and Meneveau (1999). The characteristics of the reconstructed signal depends on the (free) stretching parameters, which is related to the fractal dimension of the signal.In Scotti and Meneveau (1999), the stretching parameters was assumed to be constant in space and time and are obtained from experimental velocity signals of homogeneous and isotropic turbulence; these parameter was set to $d = \pm 2^{-1/3}$. To improve this method, we derive the stretching parameters from the Pope model spectrum, so as to reproduce both the inertial and dissipative range scales that are absent in LES.