More than 12 GW of offshore wind turbines are currently in operation in European waters. To optimise the use of the marine areas, wind farms are typically clustered in units of several hundred turbines. Understanding wakes of wind farms, which is the region of momentum and energy deficit downwind, is important for optimising the wind farm layouts and operation to minimize costs. While in most weather situations (unstable atmospheric stratification), the wakes of wind turbines are only a local effect within the wind farm, satellite imagery reveals wind-farm wakes to be several tens of kilometres in length under certain conditions (stable atmospheric stratification), which is also predicted by numerical models. The first direct in situ measurements of the existence and shape of large wind farm wakes by a specially equipped research aircraft in 2016 and 2017 confirm wake lengths of more than tens of kilometres under stable atmospheric conditions, with maximum wind speed deficits of 40%, and enhanced turbulence. These measurements were the first step in a large research project to describe and understand the physics of large offshore wakes using direct measurements, together with the assessment of satellite imagery and models.

We present an analysis of wind measurements from a series of airborne campaigns conducted to sample the wakes from two North Sea wind farm clusters, with the aim of determining the dependence of the downstream wind speed recovery on the atmospheric stability. The consequences of the stability dependence of wake length on the expected annual energy yield of wind farms in the North Sea are assessed by an engineering model. Wakes are found to extend for significantly longer downstream distances (>50 km) in stable conditions than in neutral and unstable conditions (<15 km). The parameters of one common engineering model are modified to reproduce the observed wake decay at downstream distances >30 km. More significant effects on the energy yield are expected for wind farms separated by distances <30 km, which is generally the case in the North Sea, but additional data would be required to validate the suggested parameter modifications within the engineering model. A case study is accordingly performed to show reductions in the farm efficiency downstream of a wind farm. These results emphasize not only the importance of understanding the impact of atmospheric stability on offshore wind farms but also the need to update the representation of wakes in current industry models to properly include wake-induced energy losses, especially in large offshore clusters. KEYWORDS atmospheric stability, offshore wind farm cluster, wake recovery, wind farm efficiency

A new functional form of the neutral drag coefficient for moderate to high wind speeds in the marine atmospheric boundary layer for a range of field measurements as reported in the literature is proposed. This new form is found to describe a wide variety of measurements recorded in the open ocean, coast, fetch-limited seas, and lakes, with almost one and the same set of parameters. This is the result of a reanalysis of the definition of the drag coefficient in the marine boundary layer, which finds that a constant is missing from the traditional definition of the drag coefficient. The constant arises because the neutral friction velocity over water surfaces is not directly proportional to the 10-m wind speed, a consequence of the transition to rough flow at low wind speeds. Within the rough flow regime, the neutral friction velocity is linearly dependent on the 10-m wind speed; consequently, within this rough regime, the new definition of the drag coefficient is not a function of the wind speed. The magnitude of the new definition of the neutral drag coefficient represents an upper limit to the magnitude of the traditional definition.

Eddy-covariance measurements of heat and humidity fluxes at heights of 40 m and 80 m above the sea surface in the wake of the alpha ventus wind farm in the North Sea at the FINO1 platform are presented and compared with fluxes estimated using the bulk method, which is generally applicable offshore outside of wake regions. While a clear difference is not found between bulk-estimated and eddy-covariance-derived fluxes in unstable conditions in the wake of the wind farm, a modified heat flux of between −10 W m−2 and −20 W m−2 with respect to the expected open-sea magnitudes is found within the wake during stable stratification at both measurement heights. These results demonstrate the importance of the realistic inclusion of buoyancy in modeling stable wind-farm wakes for offshore conditions and assessing their effect on the efficiency of downstream wind farms, as well as on the local climate.

A method for enhancing the calculation of turbulent kinetic energy in the Mellor-Yamada-Janjić planetary boundary-layer parametrization in the Weather Research and Forecasting numerical model is presented. This requires some unconventional selections for the closure constants and an additional stability dependent surface length scale. Single column model and three-dimensional model simulations are presented showing a similar performance with the existing boundary-layer parametrization, but with a more realistic magnitude of turbulence intensity closer to the surface with respect to observations. The intended application is an enhanced calculation of turbulence intensity for the purposes of a more accurate wind-energy forecast.