Synthetic turbulence constructed by spatially randomized fractal interpolation

Area of Science:

• Computational physics
• Fluid dynamics
• Turbulence modeling

Background:

• Fractal interpolation methods have been used to model turbulent fields.
• Previous methods had limitations in capturing the complex statistical properties of real turbulence.

Purpose of the Study:

• To propose an improved spatially randomized fractal interpolation algorithm for synthetic turbulence field generation.
• To enhance the statistical accuracy of synthetic fields compared to real turbulence.

Main Methods:

• A spatially randomized fractal interpolation algorithm is introduced.
• Random position mapping and a chosen random multiplier model for stretching factors are employed.
• A refined technique is added to model ESS scaling laws, breaking absolute scale invariance.

Main Results:

• Synthetic fields with absolute scaling properties matching SL94, K41, and MB2000 models were obtained using the Log-Poisson model.
• The refined technique successfully models turbulence fields with ESS scaling laws.
• Velocity structure functions and moments of subgrid-scale stress were precisely predicted.

Conclusions:

• The proposed algorithm generates synthetic turbulence fields with improved statistical realism.
• The method accurately captures scaling properties, including broken scale invariance.
• This approach offers a powerful tool for studying turbulence phenomena.