Urban Boundary Layers Over Dense and Tall Canopies
Alexandros Makedonas, Matteo Carpentieri, Marco Placidi
Abstract
Abstract Wind-tunnel experiments were carried out on four urban morphologies: two tall canopies with uniform height and two super-tall canopies with a large variation in element heights (where the maximum element height is more than double the average canopy height, $$h_{max}=2.5h_{avg}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>h</mml:mi> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2.5</mml:mn> <mml:msub> <mml:mi>h</mml:mi> <mml:mrow> <mml:mi>avg</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ). The average canopy height and packing density are fixed across the surfaces to $$h_{avg} = 80~\hbox {mm}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>h</mml:mi> <mml:mrow> <mml:mi>avg</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>80</mml:mn> <mml:mspace/> <mml:mtext>mm</mml:mtext> </mml:mrow> </mml:math> , and $$\lambda _{p} = 0.44$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.44</mml:mn> </mml:mrow> </mml:math> , respectively. A combination of laser Doppler anemometry and direct-drag measurements are used to calculate and scale the mean velocity profiles with the boundary-layer depth $$\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> </mml:math> . In the uniform-height experiment, the high packing density results in a ‘skimming flow’ regime with very little flow penetration into the canopy. This leads to a surprisingly shallow roughness sublayer (depth $$\approx 1.15h_{avg}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≈</mml:mo> <mml:mn>1.15</mml:mn> <mml:msub> <mml:mi>h</mml:mi> <mml:mrow> <mml:mi>avg</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ), and a well-defined inertial sublayer above it. In the heterogeneous-height canopies, despite the same packing density and average height, the flow features are significantly different. The height heterogeneity enhances mixing, thus encouraging deep flow penetration into the canopy. A deeper roughness sublayer is found to exist extending up to just above the tallest element height (corresponding to $$z/h_{avg} = 2.85$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>h</mml:mi> <mml:mrow> <mml:mi>avg</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2.85</mml:mn> </mml:mrow> </mml:math> ), which is found to be the dominant length scale controlling the flow behaviour. Results point toward the existence of a constant-stress layer for all surfaces considered herein despite the severity of the surface roughness ( $$\delta /h_{avg} = 3 - 6.25$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>h</mml:mi> <mml:mrow> <mml:mi>avg</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>-</mml:mo> <mml:mn>6.25</mml:mn> </mml:mrow> </mml:math> ). This contrasts with the previous literature.