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Monin–Obukhov similarity theory (MOST) overestimates the mean vertical velocity gradient in some atmospheric stable conditions, i.e., Richardson numberR f    0 . 1and proposes new flow similarity functions without constrainingR fto limit the overestimated velocity gradient. Next, different turbulence models based on MOST and a modified one based on the new similarity functions are investigated through numerical simulations. These turbulence models are combined with the actuator disk model (AD) and Reynolds-averaged Navier–Stokes equations (RANS) to model wind turbine wakes under stable conditions. As compared to measurements, numerical results show that turbulence models based on MOST result in a larger wake deficit and a slower wake recovery rate with a root-mean-squared error (RSME) of wake deficit in the range of 0.07 to 0.20. This overestimated wake effect is improved by applying the new similarity functions, and the RSME of wake deficit is reduced by 0.05 on average.

Monin–Obukhov Similarity Theory for Modeling of Wind Turbine Wakes under Atmospheric Stable Conditions: Breakdown and Modifications