Influence of wind direction on flow over a cliff and its interaction with a wind turbine wake

This work investigates the effect of wind direction on the flow over a cliff and its interaction with the wake of a wind turbine sited on the cliff. The cliff is modeled as a forward-facing step, and five wind directions are tested <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>(</a:mo><a:mi>θ</a:mi><a:mo>=</a:mo><a:msup><a:mn>0</a:mn><a:mo>∘</a:mo></a:msup></a:mrow><a:mo>,</a:mo><a:mo> </a:mo><a:msup><a:mn>15</a:mn><a:mo>∘</a:mo></a:msup><a:mo>,</a:mo><a:mo> </a:mo><a:msup><a:mn>30</a:mn><a:mo>∘</a:mo></a:msup><a:mo>,</a:mo><a:mo> </a:mo><a:msup><a:mn>45</a:mn><a:mo>∘</a:mo></a:msup></a:math>, and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>−</b:mo><b:msup><b:mn>45</b:mn><b:mo>∘</b:mo></b:msup><b:mrow><b:mo>)</b:mo></b:mrow></b:mrow></b:math>, where <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msup><c:mn>0</c:mn><c:mo>∘</c:mo></c:msup></c:math> represents a wind direction perpendicular to the cliff edge. The flow becomes increasingly three-dimensional with the increase in the wind direction magnitude and a cross-stream flow separation develops from the cliff leading edge. The turbulence kinetic energy decreases for wind directions higher than <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msup><d:mn>15</d:mn><d:mo>∘</d:mo></d:msup></d:math>, which is due to the absence of the streamwise flow separation for higher wind directions. The cross-stream flow development in the base flow affects the shape of the turbine wake. A two-dimensional Gaussian fit is performed on the wake velocity deficit, which shows a slight departure from self-similarity in the lateral direction. The wake recovery slows down for wind directions higher than <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msup><e:mn>15</e:mn><e:mo>∘</e:mo></e:msup></e:math>, which is consistent with the decrease in the wake growth rate for <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>θ</f:mi><f:mo>></f:mo><f:msup><f:mn>15</f:mn><f:mo>∘</f:mo></f:msup></f:mrow></f:math>. The wake shows higher deflection and tilt angle for higher wind directions. Analysis of the streamwise momentum in the wake reveals that the advection terms play a role in slowing the wake recovery for higher wind directions.