This paper reports the first turbulence measurements performed in the Long Pipe Facility at the Center for International Cooperation in Long Pipe Experiments (CICLoPE). In particular, the Reynolds stress components obtained from a number of straight and boundary-layer-type single-wire and X-wire probes up to a friction Reynolds number of 3.8×10 ⁴ are reported. In agreement with turbulent boundary-layer experiments as well as with results from the Superpipe, the present measurements show a clear logarithmic region in the streamwise variance profile, with a Townsend–Perry constant of A ₂ ≈1.26. The wall-normal variance profile exhibits a Reynolds-number-independent plateau, while the spanwise component was found to obey a logarithmic scaling over a much wider wall-normal distance than the other two components, with a slope that is nearly half of that of the Townsend–Perry constant, i.e. A _{2, w} ≈ A ₂ /2. The present results therefore provide strong support for the scaling of the Reynolds stress tensor based on the attached-eddy hypothesis. Intriguingly, the wall-normal and spanwise components exhibit higher amplitudes than in previous studies, and therefore call for follow-up studies in CICLoPE, as well as other large-scale facilities. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

The power production of the Lillgrund wind farm has been investigated by means of SCADA data covering almost 10 years of operation, wake models and numerical simulation tools, such as WindSim, OpenFOAM and ORFEUS. The analysis of the SCADA data provided the quantification of wake losses and of blockage effects, results that enable a benchmark to assess the uncertainty of other numerical methods of industrial use. The results have been analysed in terms of global array efficiency for different wind directions, wind velocity and stratification conditions. A comparison of the present results with the Jensen and Ainsle models indicated that the two used wake models are affected by an error of about 8–10% in the estimation of the array efficiency, while the error does not vary significantly when using numerical tools such as ORFEUS, WindSim and OpenFOAM. By comparing wind statistics available before the park construction, an assessment of the blockage of the Lillgrund farm was performed with contrasting results from the other numerical tools, highlighting how challenging is to assess farm blockage with current industrial settings.

A new vortex model of inviscid propeller and wind-turbine wakes is proposed based on an asymptotic expansion of the Biot–Savart induction law to account for the finite vortex core size. The circulation along the blade is assumed to be constant from the blade root to the tip approximating a turbine with maximum power production for given operating conditions. The model iteratively calculates the tip-vortex path, allowing the wake to expand/contract freely, and is afterward able to evaluate the velocity field in the whole domain. The ‘roller-bearing analogy’, proposed by Okulov and Sørensen (J. Fluid Mech., vol. 649, 2010, pp. 497–508), is used to determine the vortex core size. A comparison of the main outcomes of the present model with the general momentum theory is performed in terms of the operating parameters (namely the number of blades, the tip-speed ratio, the blade circulation and the vortex core size), demonstrating good agreement between the two. Furthermore, experimental data have been compared with the model outputs to validate the model under real operating conditions.