Recovery processes in a large offshore wind farm

Abstract

Wind turbines in a wind farm extract energy from the atmospheric flow and convert it into electricity, resulting in a localized momentum deficit in the wake that reduces energy availability for downwind turbines. Atmospheric momentum convergence from above, below, and the sides into the wakes replenishes the lost momentum, at least partially, so that turbines deep inside a wind farm can continue to function. In this study, we explore recovery processes in a hypothetical offshore wind farm with particular emphasis on comparing the spatial patterns and magnitudes of horizontal- and vertical-recovery processes and understanding the role of mesoscale processes in momentum recovery in wind farms. For this purpose, we use the Weather Research and Forecasting (WRF) model, a state-of-the-art mesoscale model equipped with a wind turbine parameterization, to simulate a hypothetical large offshore wind farm with different wind turbine spacings under realistic initial and boundary conditions. Different inter-turbine spacings range from a densely packed wind farm (case I: low inter-turbine distance of 0.5 km ∼ 5 rotor diameter) to a sparsely packed wind farm (case III: high inter-turbine distance of 2 km ∼ 20 rotor diameter). In this study, apart from the inter-turbine spacings, we also explored the role of different ranges of background wind speeds over which the wind turbines operate, ranging from a low wind speed range of 3–11.75 m s−1 (case A) to a high wind speed range of 11–18 m s−1 (case C). Results show that vertical turbulent transport of momentum from aloft is the main contributor to recovery in wind farms except in cases with high-wind-speed range and sparsely packed wind farms, where horizontal advective momentum transport can also contribute equally. Vertical recovery shows a systematic dependence on wind speed and wind farm density that is quantified using low-order empirical equations. Wind farms significantly alter the mesoscale flow patterns, especially for densely packed wind farms under high-wind-speed conditions. In these cases, the mesoscale circulations created by the wind farms can transport high-momentum air from aloft into the atmospheric boundary layer (ABL) and thus aid in recovery in wind farms. To the best of our knowledge, this is one of the first studies to look at wind farm replenishment processes under realistic meteorological conditions including the role of mesoscale processes. Overall, this study advances our understanding of recovery processes in wind farms and wind farm–ABL interactions.