A model of airflow above changes in surface heat flux,temperature and roughness for neutral and unstable conditions |
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| Authors: | P A Taylor |
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| Institution: | (1) Dept. of Mathematics, University of Toronto, Toronto, Canada |
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| Abstract: | A numerical model of airflow in the lowest 50–100 m of the atmosphere above changes in surface roughness and temperature or heat flux has been developed based on boundary layer approximations, the Businger-Dyer hypotheses for the non-dimensional wind shear and heat flux and a mixing length hypothesis.Results have been obtained for several situations, in particular, airflow with neutral upstream conditions encountering a step change in surface temperature or heat flux with no roughness change. In these cases large increases in shear stress at the outer edge of the internal boundary layer are predicted. The case of unstable upstream flow encountering a step change to zero heat flux is also considered.Two situations that may be encountered near the shores of the Great Lakes are considered.Notation
B
Businger-Dyer constant (= 16.0) in form for  M, H
-
c
p
Specific heat at constant pressure
-
g
Acceleration due to gravity
-
H
Upward vertical heat flux
-
H
0
, H
1
Surface heat fluxes for x < 0, x  0
-
k
von Kármán's constant ( = 0.4)
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l
Mixing length
-
L
Monin-Obukhov length
-
L
0
Upstream value of L
-
m
Ratio of roughness lengths (= z
1/z
0)
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RL
*
Non-dimensional parameter, see Equations (20, 22 and 24)
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RL
1
*
Same as RL
* but with z
1 scaling (= mRL
*)
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T
Scaled temperature
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T
0
(z)
Upstream temperature profile
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u
0, u
1(x)
Surface friction velocities for x < 0, x 0
-
U, W
Horizontal and vertical mean velocities
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U
0
(z)
Upstream velocity profile
-
x, z
Horizontal and vertical coordinates
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z
i
Local roughness length |
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| Keywords: | |
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