Interaction of vortex stretching with wind power fluctuations

TL;DR

This paper investigates how vortex stretching influences wind power fluctuations, proposing a scale-adaptive parameterization of subgrid-scale stresses, and analyzes wind farm data showing power-law spectra and turbulence effects.

Contribution

It introduces a scale-adaptive parameterization based on vortex stretching and the second invariant of the velocity gradient tensor for wind turbine wake modeling.

Findings

Wind power fluctuations follow a -5/3 power law spectrum.

Fluctuations depend on incoming turbulence and wake interactions.

Vortex stretching relates to energy transfer in wind turbine wakes.

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 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.