A Simulation of Scalar Transport in a Wind Turbine Wake

The push for the expansion of wind energy has resulted in an explosion of research concerning optimization of individual turbines and wind farms. Some recent studies have suggested that very large wind farms can affect global climate, and that small wind farms may actually cause changes in local meteorology. In this work we will explore how a wind turbine fundamentally affects the transport of heat and humidity near the Earth's surface on a small scale. Via direct numerical simulation (DNS), the full Navier-Stokes, energy, and scalar transport equations are solved in a turbulent boundary layer under varying thermal stratifications. The turbine wake field downstream of a wind farm is modeled by directly imposing a wake profile onto a turbulent boundary layer mean velocity and allowing the flow to then evolve with time. Since DNS is employed for this study, conservation equations are solved down to the wall allowing both turbulent and viscous transport to be evaluated. Our results indicate that heat and humidity transport increases in the wake under both neutral and unstable thermal stratification. The increase in turbulent energy downstream of the turbine promotes mixing which results in a net upward flux. Depending on the level of stratification, the surface flux of humidity can increase by as much as 10%. To further understand the processes, energy budgets and high order statistics are explored.