Gravity wave effects on wind farm efficiency

A theory of the atmospheric disturbance caused by a large wind farm is developed using a simple boundary layer (BL) representation. The model includes pressure gradients and gravity wave generation associated with a temperature inversion at the top of the BL and the normal tropospheric lapse rate aloft. The pattern of wind disturbance is computed using a Fast Fourier Transform. The slowing of the winds by turbine drag and the resulting loss of wind farm efficiency is controlled by two factors. First is the size of the wind farm in relation to the restoring effect of friction at the top and bottom of the BL. Second is the role of static stability and gravity waves in the atmosphere above the BL. The effect of the pressure perturbation is to decelerate the wind upstream and to prevent further deceleration over the wind farm with a favorable pressure gradient. As a result, the wind speed reduction is approximately uniform over the wind farm. In spite of the uniform wind over the farm, the average wind reduction is still very sensitive to the farm aspect ratio. In the special case of weak stability aloft, weak friction and the Froude Number Fr = U/root g'HT approximate to 1 the wind speed near the farm can suddenly decrease; a phenomenon we call 'choking'. Copyright (C) 2009 John Wiley & Sons, Ltd.