Fast synthesis of turbulence with multi-scale coherent vortices

Abstract: Turbulence synthesis methods often struggle to reproduce coherent vortices while capturing key statistical features. We introduce a fast synthetic turbulence method to generate instantaneous turbulent fields (termed `woven turbulence') with multi-scale vortices, combining the advantages of fractal models and coherent structures. The method generates multi-scale Burgers vortex tubes based on stochastic centerlines constructed by the fractional Brownian bridge. The largest and smallest vortices govern the integral and dissipation scales, respectively, enabling precise control over the energy spectrum across the energy-containing, inertial, and dissipation ranges. The adjustable vortex density allows tailored intermittency in velocity statistics. Remarkably, the woven turbulence achieves an extremely low computational cost, proportional to the total number of grid points. For the Taylor-Reynolds number larger than 200, its computational cost is over five orders of magnitude lower than that of direct numerical simulation (DNS). Validation against DNS data demonstrates excellent agreement in energy spectra, velocity probability distributions, and intermittency scaling. Unlike prior methods, woven turbulence simultaneously reproduces Gaussian velocity fields, Kolmogorov's five-thirds scaling for the energy spectrum, and intertwined coherent vortices akin to real turbulence. This approach not only bridges the gap between structural and statistical turbulence modelling, but also offers an efficient tool for applications requiring realistic turbulent fields.