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Airflow above changes in surface heat flux,temperature and roughness; an extension to include the stable case
Authors:P A Taylor
Institution:(1) Dept. of Mathematics, University of Toronto, Toronto, Canada
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 phgrM and phgrH.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.Notation A Refers to Taylor (1970) - B Businger-Dyer constant (= 16.0) in forms for phgr M and phgr H - C Constant in form for phgr 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, xges0 - 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, xges0 - 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 ges 0 - theta Temperature - theta 0, theta 1 Surface temperatures for x<0, xges0 - phgr E Non-dimensional absolute humidity gradient - phgr H Non-dimensional temperature gradient of heat flux - phgr M Non-dimensional wind shear - phgr phgr = phgr M = phgr H = phgr E an assumption used in stable conditions - rhov Air density - rhov Upsi Absolute humidity - rhov w Density of water - tau Kinematic shear stress - zeta Logarithmic height scale (= ln(z+z 1)/z 1)
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