On the probability distribution function of the velocity field and its derivative in multi-scale turbulence

Using a combination of active and passive grids, we produce an inhomogeneous turbulent flow with strongly non-Gaussian velocity probability distribution (density) functions (pdfs). This new, multi-scale flow shares features with the turbulent jet in freestream turbulence, the near field of turbulence-generating grids, and atmospheric flows. In particular, we study unskewed velocity distributions with both super- and sub-Gaussian tails and demonstrate the linear dependence of the normalized odd and even moments of the distributions on the first and second spatial derivatives of the turbulence r.m.s. fields, respectively. We also note bimodal behavior of the pdfs. The experiments demonstrate a clear effect of the flow organization and the large-scale intermittency on the velocity derivative pdfs and the small scales of the turbulence. The work is motivated by the complex wind fields, and associated, intermittent high stresses, encountered by wind turbines. We also draw comparisons to recent studies of multi-scale turbulence produced by fractal grids.