Wind turbine boundary layer arrays for Cartesian and staggered configurations: Part II, low-dimensional representations via the proper orthogonal decomposition

Cartesian and row-offset wind turbine array configurations were tested investigating the wake interaction and recovery dynamics. The snapshot proper orthogonal decomposition is applied to velocity measurements. Resulting modes are used in constructing low-dimensional descriptions of turbulence statistics including the turbulence kinetic energy production and the flux of turbulence kinetic energy. Descriptions of the turbulent behavior are made on the basis of the span of the streamwise average profile of the Reynolds shear stress, -(uv) over bar, with the addition of orthogonal modes. The Reynolds stress criterion was selected for the convergence of the model as it is a good representation of the range of turbulent dynamics in the wake of a wind turbine. The description demonstrates that the turbulence kinetic energy production and the flux of turbulence kinetic energy are accurately rebuilt with approximately 1% of the total resultant orthogonal modes. Structures associated with the top-tip of the rotor blade reconstruct with fewer modes than those associated with the bottom-tip of the rotor or the nacelle. This confirms that the greatest part of the turbulence kinetic energy is located high in the turbine canopy as described by the turbulent stresses. Overall, behavior of individual turbines in recovered positions within the arrays requires fewer modes to converge than those in locations with less recovered inflows. Copyright (c) 2014 John Wiley & Sons, Ltd.