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Airflow above changes in surface heat flux, temperature and roughness; an extension to include the stable case

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Abstract

A numerical model of airflow above changes in surface roughness and thermal conditions is extended to include cases with stable thermal stratification within the internal boundary-layer. The model uses a mixing-length approach with empirical forms for φM and φH.

Results are presented for some basic cases and an attempt is then made to compare results given by the model with the experimental results of Rider, Philip and Bradley. Tolerable agreement is achieved. The importance of roughness change and thermal stability effects in the diffusion of heat and moisture near a leading edge is emphasised.

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Abbreviations

A:

Refers to Taylor (1970)

B :

Businger-Dyer constant (= 16.0) in forms for φ M and φ H

C :

Constant in form for φ in stable case

c p :

Specific heat at constant pressure

E :

Scaled absolute humidity

g :

Acceleration due to gravity

H :

Upward vertical heat flux

H 0, H 1 :

Surface heat fluxes for x <0, x⩾0

H E :

Upward latent heat flux

k :

Von Kármán's constant (= 0.4)

K H :

K W Eddy transfer coefficients for heat and water vapour

L :

Monin-Obukhov length

L H :

Latent heat of evaporation for water

m :

Ratio of roughness lengths ( = z 1/z 0)

RPB:

Refers to Rider et al. (1964)

RL*:

Non-dimensional parameter (see Equations (9), (20a), (22a), (24a))

R*:

Net radiation less ground heat flux (see Equations (15), (16))

T :

Scaled temperature

T 1 :

Downstream scaled surface temperature

u 0 u 1(x):

Surface friction velocities for x <0, x⩾0

U, W :

Horizontal and vertical mean velocities

x, z :

Horizontal and vertical co-ordinates

Z i :

Local roughness length

z 0, z i :

Roughness lengths for x < 0, x ⩾ 0

θ :

Temperature

θ 0, θ 1 :

Surface temperatures for x<0, x⩾0

φ E :

Non-dimensional absolute humidity gradient

φ H :

Non-dimensional temperature gradient of heat flux

φ M :

Non-dimensional wind shear

φ φ = φ M = φ H = φ E :

an assumption used in stable conditions

ϱ :

Air density

ϱ ϒ :

Absolute humidity

ϱ w :

Density of water

τ:

Kinematic shear stress

ζ:

Logarithmic height scale (= ln(z+z 1)/z 1)

References

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  • Philip, J. R.: 1959, ‘The Theory of Local Advection, 1’, J. Meteorol. 16, 535–547.

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Authors and Affiliations

  1. Dept. of Mathematics, University of Toronto, Toronto, Canada

    P. A. Taylor

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  1. P. A. Taylor
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Taylor, P.A. Airflow above changes in surface heat flux, temperature and roughness; an extension to include the stable case. Boundary-Layer Meteorol 1, 474–497 (1971). https://doi.org/10.1007/BF00184785

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  • DOI: https://doi.org/10.1007/BF00184785

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