Three-dimensional synthetic turbulence constructed by spatially randomized fractal interpolation

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A spatially randomized fractal interpolation algorithm to construct three-dimensional synthetic turbulence from original coarse field is reported. As in the one-dimensional case by Ding et al. (Phys. Rev. E 82, 036311, 2010), during the fractal interpolation, positions mapping between large and small scale cubes are chosen randomly, and the stretching factors are drawn from a log-Poisson random multiplicative process. A linear combination function defined as the base part in fractal interpolation and a theoretical energy spectrum model for fully developed turbulence are introduced into the procedure. Statistical analysis shows that the synthetic field displays some properties very close to the direct numeric simulated field, such as probability distributions of velocity, velocity gradient, velocity increment, and the anomalous scaling behavior of the longitude velocity structure functions, which follows the SL94 model precisely. After a short time using direct numeric simulation with the synthetic field as initial data, the typical local dynamical structures described by the teardrop shape of the Q-R plane for empirical turbulence can be reproduced.