• internal boundary layer
• top-down model
• wind farms

The current work focuses on the structure of the internal boundary layer over long wind farms.
Hot-wire measurements have been performed providing time-resolved data for the computation of velocity statistics and spectra. Inline and staggered layouts with and without free-stream turbulence have been characterised in detail above the turbine canopy.
New relations for the turbulent shear stress and for the vertical flux of the mean kinetic energy are proposed by means of an integral analysis of the governing equation (averaged in time and space) above the wind farm. The aim is to quantify the flux of energy replenishing the kinetic energy at the turbine level and characterise the evolution of the internal boundary layer. it was found that the the vertical flux of energy are composed by a turbulent energy flux (proportional to the Reynolds stress and the local momentum) and an advection term of the kinetic energy imparted by the vertical velocity. The latter has been found to be equally important as the turbulent flux throughout the entire length of the farm and therefore cannot be neglected if an estimation of the total energy flux is desired such as, for instance, in “top-down” models.
A self-similar analysis of the velocity profile indicate that the mean velocity deficit profile is self similar and scales with the velocity deficit on top of the canopy and with a characteristic thickness of the velocity deficit profile. The shear stress profile seems to follow a similar scaling although with a slightly worse agreement.
A spectral analysis has been performed providing the energy distribution at the different scales of the turbulent motion.
A characteristic frequency above the farm is visible throughout the farm length with a value of
St = 0.12
The Strouhal number appears to be of the same order of the one observed in the literature about wake meandering, that should be therefore considered as the leading dynamical phenomenon in a large farm that builds up already after the first 2-3 rows of turbine and that overwhelms the tip-vortex signature observed only behind the first row of turbines and that looses abruptly coherence and strength due to the turbulent environment.