  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 that
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, POD analysis
indicates that the wind power fluctuations depend on the incoming turbulence
and its modulation by the wake interactions in wind farms.
