Analytical prediction of the start of a wind turbine far wake considering the balance between pressure and Reynolds stresses

Abstract Near-wake modelling is an important component in turbine wake modelling, and it has received increased attention in recent years. This study derives an analytical model based on an actuator disc model which considers near-wake mixing effect to determine both the velocity profile and the starting position of the far wake. The model assumes axisymmetrical Gaussian far-wake profiles and evaluates the Reynolds shear stresses using the Boussinesq eddy viscosity hypothesis. The start of the far-wake region is defined as the position where the centreline velocity starts to recover at a decelerating rate, and this position is found approximately by relating pressure and Reynolds stresses without empirical parameters. A series of Reynolds-averaged Navier-Stokes (RANS) simulation results over a range of inflow turbulence conditions are used to validate the model. The results show good agreements between the proposed model and the simulation data.