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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- A * :
temperature change stability parameter
- B :
- 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 :
- 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 :
- L :
modified Obukhov stability length
- q :
- 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 :
- 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 :
- w :
- W :
total average vapor flux (E w averaged over the fetch)
- x :
horizontal, downwind axis
- x 0 :
- z :
- z 0 :
- λ :
- ϱ :
- 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
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Cite this article
Weisman, R.N. A developing boundary layer over an evaporating surface. Boundary-Layer Meteorol 8, 437–445 (1975). https://doi.org/10.1007/BF02153562
- Boundary Layer
- Surface Temperature
- Diffusion Equation
- Conservation Equation
- Sudden Change