The superposition of a rotating wake with the atmospheric Ekman spiral 
Journal Article
Overview
abstract
<p align="justify"><span>Stably stratified atmospheric boundary layers are often characterized by a veering wind profile, in which the wind direction changes clockwise (counterclockwise) with height in the Northern Hemisphere (Southern Hemisphere). Wind-turbine wakes respond to this veer in the incoming wind by stretching from a circular shape into an ellipsoid. Englberger, D&#246;rnbrack and Lundquist (2020) investigate the relationship between this stretching and the direction of the turbine rotation by means of large-eddy simulations </span><span>(LESs)</span>.</p><p align="justify"><span>The basic physics underlying the interaction process of a rotating </span><span>wake</span><span> with a veering inflow can be described with the superposition of a Rankine vortex as representation of the wind-turbine </span><span>wake</span><span> with the characteristic </span><span>hemispheric-dependent </span><span>nighttime Ekman spiral of the atmospheric wind. </span><span>In dependence of the rotational direction </span><span>an</span><span>d</span><span> the hemisphere, this</span><span> superposition results in an amplification of the spanwise flow component if a </span><span>counterclockwise</span><span> rotating </span><span>rotor interacts with a northern hemispheric Ekman spiral </span><span>(</span><span>a clockwise rotating rotor interacts with a southern hemispheric Ekman spiral</span><span>)</span><span>. In case of a clockwise rotating rotor interacting with a northern hemispheric Ekman spiral </span><span>(</span><span>a counterclockwise rotating </span> <span>rotor interacting with a southern hemispheric Ekman spiral</span><span>)</span><span>, the superposition leads to a weakening of the spanwise flow component. In case of no veering inflow, the magnitude of the spanwise flow component is independent of the rotational direction.</span></p><p align="justify"><span>Th</span><span>ese theoretical</span> <span>superposition </span><span>effect</span><span> of the Ekman layer with the wake vortex </span><span>occur in nighttime </span><span>LESs, </span><span>where t</span><span>he rotational direction dependent magintude of the spanwise flow component further impacts the streamwise flow component in the wake. In particular, </span><span>there is a rotational direction dependent difference in </span><span>the </span><span>wake strength, </span><span>the </span><span>extension </span><span>of the wake</span><span>, </span><span>the wake </span><span>width, and </span><span>the wake </span><span>deflection </span><span>angle. </span><span>In more detail, a </span><span>northern hemispheric </span><span>veering wind in combination with a counterclockwise rotating actuator results in a larger streamwise velocity output, a larger spanwise wake width, and a larger wake deflection angle at the same downwind distance in comparison to a clockwise rotating turbine.</span></p><p><span>Englberger, D&#246;rnbrack and Lundquist, 2020, Does the rotational direction of a wind turbine impact the wake in a stably stratified atmospheric boundary layer? </span><span><em>Wind Energ. Sci. </em></span><span><strong>5</strong></span><span>, 1359-1374.</span></p>
