Richard J.A.M. Stevens

Physics of Fluids · University of Twente

Publication 99 · Wind-farm flow

Analytical model of fully developed wind farms in conventionally neutral atmospheric boundary layers

C. Li, L. Liu, X. Lu, R.J.A.M. Stevens, J. Fluid Mech. 948, A43 (2022).

Main finding

Boundary-layer height defined where total stress falls to 5% of its surface value follows a CNBL scaling with fitted constant near 1.61; inversion height is about 0.9h with corresponding constant near 1.45. Geostrophic drag-law coefficients depend on stability parameter but differ from flat-terrain values because wind-farm drag is larger.

Hub-height wind speed and power against stability parameter for aligned and staggered farms
How to read the figure. Hub-height wind speed normalised by the geostrophic wind (top) and turbine power (bottom) against the free-atmosphere stability parameter, for aligned (left) and staggered (right) farms at three latitudes. Lines are the analytical model, symbols the large-eddy simulations. Both quantities depend on stability, and the model follows that dependence across the range. Open the full-resolution figure. Figure 7. C. Li et al. (2022). No separate licence is stated here; consult the original publication and credited source before reuse.

Why this matters

Supports a conditional CNBL system optimum and demonstrates that atmospheric depth/rotation enter farm power.

Research context

The joined model closes the momentum pathway from geostrophic forcing through boundary-layer drag to the turbine layer. Its constants are calibrated and assessed on the same LES family, one spacing, and two layouts.

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