Turbulence characteristics of a thermally stratified wind turbine array boundary layer via proper orthogonal decomposition

A large eddy simulation framework is used to explore the structure of the turbulent flow in a thermally stratified wind turbine array boundary layer. The flow field is driven by a constant geostrophic wind with time-varying surface boundary conditions obtained from a selected period of the CASES-99 field experiment. Proper orthogonal decomposition is used to extract coherent structures of the turbulent flow under the considered thermal stratification regimes. The flow structure is discussed in the context of three-dimensional representations of key modes, which demonstrate features ranging in size from the wind turbine wakes to the atmospheric boundary layer. Results demonstrate that structures related to the atmospheric boundary layer flow dominate over those introduced by the wind farm for the unstable and neutrally stratified regimes; large structures in atmospheric turbulence are beneficial for the wake recovery, and consequently the presence of the turbulent wind turbine wakes is diminished. Contrarily, the flow in the stably stratified case is fully dominated by the presence of the turbines and highly influenced by the Coriolis force. A comparative analysis of the test cases indicates that during the stable regime, higher-order modes contribute less to the overall character of the flow. Under neutral and unstable stratification, important turbulence dynamics are distributed over a larger range of basis functions. The influence of the wind turbines on the structure of the atmospheric boundary layer is mainly quantified via the turbulence kinetic energy of the first ten modes. Linking the new insights into structure of the wind turbine/atmospheric boundary layer and their interaction addressed here will benefit the formulation of new simplified models for commercial application.