A Novel Velocity Spectrum Model Incorporating Long-Range Dependence and Fractal Features

Quantifying key processes in turbulent flows across different scales is essential in many engineering and scientific fields, particularly for analyzing unsteady aerodynamics and hydrodynamics. Traditional velocity spectra models often fall short in representing critical energy-containing regions over a broad range of scales. We present a novel spectral model that accurately characterizes velocity spectra across various scales to overcome these limitations. This new model is defined by a five-parameter covariance function, where each parameter has a

distinct physical interpretation and a clear method for its determination. Adjusting these five parameters can effectively control the variance and the low, high, and intermediate frequencies within the spectral distribution. This capability allows for decoupling the Hurst effect and fractal behavior at low and high frequencies. We validate the model using field data from tidal currents and atmospheric boundary layer (ABL) flows, demonstrating its robustness and effectiveness in capturing scaling behaviors in different regions. This model offers flexibility and adaptability that are not possible in classical turbulent spectrum models, such as the von Kármán and IEC Kaimal spectrum models.