Wind-farm wake recovery mechanisms in conventionally neutral boundary layers

TL;DR

This study investigates how wind-farm wakes behave and recover in different boundary layer conditions, revealing the influence of boundary layer depth on wake deflection, recovery rate, and flow dynamics through modeling and analysis.

Contribution

It introduces a simple velocity profile model and detailed momentum analysis to understand wind-farm wake mechanisms in various boundary layer depths, highlighting the role of turbulent entrainment.

Findings

Deep boundary layers enhance wake recovery via vertical entrainment.

Shallow boundary layers cause anticlockwise wake deflection and limited vertical mixing.

Wake narrows downstream in all boundary layer conditions.

Abstract

Synthetic-aperture radar images and mesoscale model results show that wind-farm wakes behave very differently than single-turbine wakes, e.g. with wakes that seemingly narrow and do not disperse over long distances. In the current work, we aim at better understanding the physical mechanisms that govern wind-farm wake behaviour and recovery. Hence, we study the wake properties of a 1.6 GW wind-farm operating in conventionally neutral boundary layers with four capping-inversion heights, i.e. 203, 319, 507 and 1001 m. In shallow boundary layers, we find strong flow decelerations which reduce the Coriolis force magnitude, leading to an anticlockwise wake deflection in the Northern Hemisphere. In deep boundary layers, the vertical turbulent entrainment of momentum adds clockwise-turning flow from aloft into the wake region, leading to a faster recovery rate and a clockwise wake deflection. To estimate the wake properties, we develop a simple model that fits the velocity magnitude profiles along the spanwise direction. Based on this, we observe that the wake narrows along the downstream direction in all cases. Further, a detailed momentum budget analysis shows that the wake is mostly replenished by turbulent vertical entrainment in deep boundary layers. In shallow boundary layers, the capping inversion limits vertical motions and wakes are mostly replenished by mean flow entrainment in the spanwise direction. Moreover, in these cases, we observe a counterclockwise flow rotation near the left edge of the wake, which persists at each location downstream of the farm, giving rise to local strong streamwise velocity gradients along the spanwise direction.