Atmospheric pressure gradients and Coriolis forces provide geophysical limits to power density of large wind farms

The geophysical limit to maximum land-area power density of large wind farms is related to the rate of replenishment of kinetic energy removed from the atmosphere by wind turbines. Although observations and numerical simulations have indicated an upper bound to the power density in the order of 1 W/m(2), no theoretical foundation has yet been provided. Here, we study the role of atmospheric pressure gradients and the latitude-dependent Coriolis parameter in the power density of large-scale wind farms by means of both numerical atmospheric simulations and analytic expressions. We illustrate that energy transport to regional-scale wind farms is primarily governed by horizontal pressure gradients and their interaction with the Coriolis force and turbine-induced surface drag within the latitude-dependent Ekman layer. Higher pressure gradients and lower Coriolis parameters promote higher energy availability and, consequently, higher potential power density, suggesting that the power density of regional-scale wind farms is largely resource- and location-dependent.