Synthetic Turbulence Constructed by Self-Learning Fractal Interpolation

A self-learning fractal interpolation algorithm to construct synthetic fields with statistical properties close to real turbulence is proposed. Different from our previous work [ Phys. Rev. E 84 (2011) 026328 , 82 (2010) 036311 ], the position mapping and stretching factors between the adjacent large and small scales are learned from the initial information. Using this method, a turbulence-like field with K41 spectra and without dissipation is constructed well through a coarse grid velocity signal from one experiment's data. After filtering the interpolated signal appropriately, the probability distribution of velocity, velocity structure functions and the anomalous scaling law of the synthetic field are close to those of the original signal.