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eTheses Repository - University of Birmingham

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3.2.1 Calculation <strong>of</strong> dynamical effects<br />

The dynamical effects due to buildings calculated by BEP are:<br />

• Loss <strong>of</strong> momentum due to horizontal surfaces (ro<strong>of</strong>s and canyon floors) inducing a<br />

frictional force. For this term the classic surface layer (MOST) formulae <strong>of</strong> Louis<br />

(1979) are used to calculate the momentum flux for the horizontal surfaces. This<br />

term is however vertically distributed from ground to the highest building, and is<br />

H<br />

proportional to the fractional area <strong>of</strong> the horizontal surface in the grid cell S . The<br />

turbulent momentum flux at level iu due to the horizontal surfaces is:<br />

r<br />

Fu<br />

H<br />

iu<br />

k<br />

= −ρ<br />

∆z<br />

[ln(<br />

z<br />

2<br />

IU<br />

oiu<br />

/ 2<br />

)]<br />

2<br />

f<br />

m<br />

∆z<br />

(<br />

z<br />

IU<br />

oiu<br />

/ 2<br />

, Ri<br />

B<br />

) U<br />

hor<br />

IU<br />

r<br />

U<br />

IU<br />

S<br />

H<br />

IU<br />

iu<br />

(Equation 3.9)<br />

where k is the von Karmen constant (0.4), fm comes from Louis (1979), RiB is the<br />

hor<br />

bulk Richardson number calculated at level IU, and U is the horizontal wind<br />

component.<br />

• Exchange <strong>of</strong> momentum through the vertical surfaces (walls) due to pressure and<br />

viscous drag forces induced by the presence <strong>of</strong> buildings on the flow. The<br />

momentum flux due to the vertical surfaces is:<br />

r<br />

Fu<br />

V<br />

IU<br />

r<br />

ort ort V<br />

= −ρC<br />

d U IU U IU S IU<br />

(Equation 3.10)<br />

IU<br />

69

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