A novel vector potential random flow generation method for synthesizing divergence-free homogeneous isotropic turbulence with arbitrary spectra

A novel method, known as the vector potential random flow generation (VPRFG) method, is introduced for synthesizing divergence-free homogeneous isotropic turbulence with arbitrary spectra. First, the proposed approach employs the random-flow-generation-based method to create a vector potential field. Subsequent application of the curl operation to this field produces a turbulent flow that inherently satisfies the divergence-free condition. In the formulas of the proposed method, we explicitly impose arbitrary homogeneous isotropic three-dimensional spatial cross-spectral density (CSD) and Taylor's frozen hypothesis. This ensures that the generated turbulence conforms to prescribed statistical characteristics, including energy spectra, one-dimensional spatial power spectral density (PSD), temporal PSD, spatial coherence function, turbulent kinetic energy, and Reynolds stress. Additionally, the theoretical accuracy of the proposed method is validated through numerical examples, employing the von Kármán energy spectrum as the target value. Finally, large eddy simulations of homogeneous isotropic temporal-decaying box turbulence generated by the VPRFG method demonstrate a close alignment with the experimental results.