The superposition of a rotating wake with the atmospheric Ekman spiral&#160;
Authors: Englberger Antonia , Dörnbrack Andreas , Lundquist Julie K. 
Published: March 2021

&lt;p align=&quot;justify&quot;&gt;&lt;span&gt;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&amp;#246;rnbrack and Lundquist (2020) investigate the relationship between this stretching and the direction of the turbine rotation by means of large-eddy simulations &lt;/span&gt;&lt;span&gt;(LESs)&lt;/span&gt;.&lt;/p&gt;&lt;p align=&quot;justify&quot;&gt;&lt;span&gt;The basic physics underlying the interaction process of a rotating &lt;/span&gt;&lt;span&gt;wake&lt;/span&gt;&lt;span&gt; with a veering inflow can be described with the superposition of a Rankine vortex as representation of the wind-turbine &lt;/span&gt;&lt;span&gt;wake&lt;/span&gt;&lt;span&gt; with the characteristic &lt;/span&gt;&lt;span&gt;hemispheric-dependent &lt;/span&gt;&lt;span&gt;nighttime Ekman spiral of the atmospheric wind. &lt;/span&gt;&lt;span&gt;In dependence of the rotational direction &lt;/span&gt;&lt;span&gt;an&lt;/span&gt;&lt;span&gt;d&lt;/span&gt;&lt;span&gt; the hemisphere, this&lt;/span&gt;&lt;span&gt; superposition results in an amplification of the spanwise flow component if a &lt;/span&gt;&lt;span&gt;counterclockwise&lt;/span&gt;&lt;span&gt; rotating &lt;/span&gt;&lt;span&gt;rotor interacts with a northern hemispheric Ekman spiral &lt;/span&gt;&lt;span&gt;(&lt;/span&gt;&lt;span&gt;a clockwise rotating rotor interacts with a southern hemispheric Ekman spiral&lt;/span&gt;&lt;span&gt;)&lt;/span&gt;&lt;span&gt;. In case of a clockwise rotating rotor interacting with a northern hemispheric Ekman spiral &lt;/span&gt;&lt;span&gt;(&lt;/span&gt;&lt;span&gt;a counterclockwise rotating &lt;/span&gt; &lt;span&gt;rotor interacting with a southern hemispheric Ekman spiral&lt;/span&gt;&lt;span&gt;)&lt;/span&gt;&lt;span&gt;, 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.&lt;/span&gt;&lt;/p&gt;&lt;p align=&quot;justify&quot;&gt;&lt;span&gt;Th&lt;/span&gt;&lt;span&gt;ese theoretical&lt;/span&gt; &lt;span&gt;superposition &lt;/span&gt;&lt;span&gt;effect&lt;/span&gt;&lt;span&gt; of the Ekman layer with the wake vortex &lt;/span&gt;&lt;span&gt;occur in nighttime &lt;/span&gt;&lt;span&gt;LESs, &lt;/span&gt;&lt;span&gt;where t&lt;/span&gt;&lt;span&gt;he rotational direction dependent magintude of the spanwise flow component further impacts the streamwise flow component in the wake. In particular, &lt;/span&gt;&lt;span&gt;there is a rotational direction dependent difference in &lt;/span&gt;&lt;span&gt;the &lt;/span&gt;&lt;span&gt;wake strength, &lt;/span&gt;&lt;span&gt;the &lt;/span&gt;&lt;span&gt;extension &lt;/span&gt;&lt;span&gt;of the wake&lt;/span&gt;&lt;span&gt;, &lt;/span&gt;&lt;span&gt;the wake &lt;/span&gt;&lt;span&gt;width, and &lt;/span&gt;&lt;span&gt;the wake &lt;/span&gt;&lt;span&gt;deflection &lt;/span&gt;&lt;span&gt;angle. &lt;/span&gt;&lt;span&gt;In more detail, a &lt;/span&gt;&lt;span&gt;northern hemispheric &lt;/span&gt;&lt;span&gt;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.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;Englberger, D&amp;#246;rnbrack and Lundquist, 2020, Does the rotational direction of a wind turbine impact the wake in a stably stratified atmospheric boundary layer? &lt;/span&gt;&lt;span&gt;&lt;em&gt;Wind Energ. Sci. &lt;/em&gt;&lt;/span&gt;&lt;span&gt;&lt;strong&gt;5&lt;/strong&gt;&lt;/span&gt;&lt;span&gt;, 1359-1374.&lt;/span&gt;&lt;/p&gt;