Interaction of vortex stretching with wind power fluctuations

Abstract

The transfer of turbulence kinetic energy from large to small scales occurs through vortex stretching. Also, statistical properties of the subgrid-scale energy fluxes depend on the alignment of the vorticity vector with the principal strain axis. A heuristic analysis of the present study indicates that vortex-stretching and the second invariant of the velocity gradient tensor provide a scale-adaptive parameterization of the subgrid-scale stresses and the local energy fluxes in the wakes of wind turbines. The scale-adaptivity underlies the restricted Euler dynamics of the filtered motion where vortex-stretching plays in the growth of the second invariant of filtered velocity gradient and the local energy transfer. We have analyzed wind power fluctuations in a utility-scale wind farm with 41 actuator disks. The numerical results show that the spectrum of the wind power fluctuations follows a power law with a logarithmic slope of −5/3. Furthermore, a brief analysis with the proper orthogonal decomposition method indicates that the maximum variability of wind power fluctuations depends on the incoming turbulence and its modulation by the wake interactions in wind farms.