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A developing boundary layer over an evaporating surface

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Abstract

The problem of air flow over a sudden change in surface temperature and humidity has been solved using mixing-length theory. The method is similar to that used by P. A. Taylor (1970) with some modifications. The form of the mixing length suggested by Blackadar is used and this allows calculation farther downwind. A vapor diffusion equation is included in the set of conservation equations and a vapor buoyancy term is included in the stability length. The vapor buoyancy is found to enhance significantly the turbulent diffusion but to a lesser degree than does the thermal buoyancy.

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Abbreviations

A * :

temperature change stability parameter

B :

Businger-Dyer constant

B * :

specific humidity change stability parameter

c p :

specific heat at constant pressure

E :

vapor flux at a point,E (x, z)

E w :

vapor flux at the surface

f :

Coriolis parameter

g :

acceleration of gravity

H :

sensible heat flux at a point,H (x, z)

k :

von Kármán's constant

K H, V, M :

turbulent diffusivities of heat, vapor and momentum, respectively

l :

mixing length

L :

modified Obukhov stability length

q :

specific humidity

q a :

specific humidity upwind of discontinuity

q a 0 :

specific humidity at the surface, upwind of discontinuity

q w :

specific humidity downwind of discontinuity

T :

temperature

T α :

temperature upwind of discontinuity

T a 0 :

temperature at the surface, upwind of discontinuity

T w :

temperature of water surface, downwind of discontinuity

u :

x-direction velocity component

u * :

friction velocity at a point,u * (x, z)=√Τϱ

u a* :

friction velocity upwind of discontinuity

V g :

geostrophic wind

w :

z-direction velocity

W :

total average vapor flux (E w averaged over the fetch)

x :

horizontal, downwind axis

x 0 :

fetch

z :

vertical axis

z 0 :

roughness length

λ :

scaling height

ϱ :

air density

Τ :

shear stress or vertical momentum flux at a point

Τ w :

shear stress at the surface and in the wall layer

ϕ M, H, V :

dimensionless shear stress, heat flux, and vapor flux, respectively

References

  1. Blackadar, A. K.: 1962, ‘The Vertical Distribution of Wind and Turbulent Exchange in a Neutral Atmosphere’,J. Geophys. Res. 67, 3095–3102.

  2. Businger, J. A.: 1966, ‘Transfer of Momentum and Heat in the Planetary Boundary Layer’, Proc. Arctic Heat Budget and Atmospheric Circulation, Rand Corp, RM-5233-NSF.

  3. Dyer, A. J.: 1967, ‘The Turbulent Transport of Heat and Water Vapor in an Unstable Atmosphere’,Quart. J. Roy. Meteorol. Soc. 96, 715–721.

  4. Monin, A. S. and Yaglom, A. M.: 1971,Statistical Fluid Mechanics, MIT Press, Cambridge, Mass.

  5. Obukhov, A. M.: 1946, ‘Turbulence in an Atmosphere with a Nonuniform Temperature’, Trudy Instit. Teoret. Geoflz. AN —SSR, No. 1 (English translation:Boundary-Layer Meteorol. 2, 1971).

  6. Petersen, E. L. and Taylor, P. A.: 1973, ‘Some Comparisons Between Observed Wind Profiles at Risa and Theoretical Predictions for Flow over Inhomogeneous Terrain’,Quart. J. Roy. Meteorol. Soc. 99, 329–336.

  7. Plate, E. J.: 1971, ‘Aerodynamic Characteristics of Atmospheric Boundary Layers’, U.S. Atomic Energy Commission Critical Review Series.

  8. Shir, C. C.: 1972, ‘A Numerical Computation of Air Flow over a Sudden Change of Surface Roughness’,J. Atmospheric Sci. 29, 304–310.

  9. Taylor, P. A.: 1970, ‘A Model of Airflow above Changes in Surface Heat Flux, Temperature and Roughness for Neutral and Unstable Conditions’,Boundary-Layer Meteorol. 1, 18–39.

  10. Weisman, R. N. and Brutsaert, W.: 1973, ‘Evaporation and Cooling of a Lake Under Unstable Atmospheric Conditions’,Water Resources Res. 9, 1242–1257.

  11. Wu, S. S.: 1965, ‘A Study of Heat Transfer Coefficients in the Lowest 400 Meters of the Atmosphere’,J. Geophys. Res. 70, 1801–1807.

  12. Zilitinkevich, S. S.: 1966, ‘Effect of Humidity, Stratification on Hydrostatic Stability’,Izv. Acad. Sci. Atmos. Oceanic Phys. 2, 1089–1094, (English Trans. AGU, 655–568).

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Weisman, R.N. A developing boundary layer over an evaporating surface. Boundary-Layer Meteorol 8, 437–445 (1975). https://doi.org/10.1007/BF02153562

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Keywords

  • Boundary Layer
  • Surface Temperature
  • Diffusion Equation
  • Conservation Equation
  • Sudden Change