01 Jun 2023
 | 01 Jun 2023
Status: a revised version of this preprint is currently under review for the journal WES.

The wind farm pressure field

Ronald Smith

Abstract. The disturbed atmospheric pressure near a wind farm arises from the turbine drag forces in combination with vertical confinement associated with atmospheric stability. These pressure gradients slow the wind upstream, deflect the air laterally, weaken the flow deceleration over the farm and modify the wake recovery. Here, we describe the airflow and pressure disturbance near a wind farm under typical stability conditions and alternatively, with the simplifying assumption of a rigid lid. The rigid lid case clarifies the cause of the pressure disturbance and its close relationship to wind farm drag.

The key to understanding the rigid lid model is the proof that the pressure field p(x,y) is a Harmonic Function almost everywhere. It follows that the maximum and minimum pressure occur at the front and back edge of the farm. Over the farm, the favorable pressure gradient is constant and significantly offsets the turbine drag. Upwind and downwind of the farm, the pressure field is a dipole given by p(x,y)≈Axr−2 where the coefficient A is proportional to the total farm drag. Two derivations of this law are given. Field measurements of pressure can be used to find the coefficient A and thus to estimate total farm drag.

Ronald Smith

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Ronald Smith

Ronald Smith


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Short summary
Recent papers have investigated the impact of turbine drag on local wind patterns but these studies have not given a full explanation of the induced pressure field. The pressure field blocks, deflects and in other ways modifies farm efficiency. Current “gravity wave” models are complex and provide no estimation tools. We dig deeper into the cause of the pressure field and provide approximate closed form expressions for back-of-the-envelope predictions of pressure field effects.