Three-dimensional synthetic turbulence constructed by spatially randomized fractal interpolation.

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.

Synthetic turbulence constructed by spatially randomized fractal interpolation.

A spatially randomized fractal interpolation algorithm to construct synthetic fields with statistical properties close to real turbulence is proposed. It improves the previous works on fractal interpolation so that the position mapping between large and small scales is chosen randomly and the stretching factors are drawn from any chosen random multiplier model. In particular, using different parameters of Log-Poisson model, synthetic fields with absolute scaling properties close to SL94 model (for fully developed turbulence), K41 model and MB2000 model (for magnetohydrodynamic turbulence) are obtained, respectively. To model real turbulence fields which do not obey absolute scaling laws but ESS scaling laws, a refined technique is added. It is shown that both the velocity structure functions and the moments of subgrid-scale stress can be precisely predicted when the scale invariance is broken.