Von Kármán's Constant in Atmospheric Boundary Layer Flow: Reevaluated

View More View Less
  • 1 Department of Meteorology, S-751 20 Uppsala, Sweden
© Get Permissions
Restricted access

Abstract

A field experiment has been carried out with the specific objective in mind to determine the value of von Kármán's constant in atmospheric boundary layer flow, and also to investigate its possible dependence on the surface Rossby number Ro0. Data from three field measurement campaigns at Marsta, Sweden, were used in the analysis. Depending on the ground cover: deep snow (40 cm), plowed field or 15–20 cm high wheat crop the surface roughness in the three campaigns was respectively: 1 mm, 7.5 mm and 24 mm. The corresponding range in Ro0 is roughly 2.5×106−6.5×107.

In the experiment a turbulence instrument was used (the MIUU instrument) that has been carefully examined for aerodynamic error effects and duly corrected. Measurements of turbulent fluxes made with this instrument at ca. 2 and 6 m above the surface were used, together with wind profile measurements. Data from the measurements with the turbulence instruments were also used to correct the cup anemometers for overspeeding (found to be 5%).

In all, 16 hours of measurements were used for the analysis. These runs have been selected on the basis of stringent criteria on fetch requirements and minimum wind-speed required. The runs represent near neutral or slightly stable conditions (−0.04≤z/L<0.1). The quantity studied is ϕ′m=(0.4/k)ϕ(z/L)=0.4/k(∂u¯/∂zkz/u*, evaluated at z=2 m but with u* and L extrapolated to z=0 m.

The analysis gives as a result that k=0.40±0.01, with no evidence of a variation with the surface Rossby number within the range of Ro0-values encountered (2.5×106−6.5×107). This finding is in agreement with recent laboratory studies by Purtell et al. (1981), which indicate that k is independent of Reynolds number and equal to 0.41. As a by-product the constant B in the relation ϕm=1+Bz/L is determined to be 4.0 within the limited stability range encountered.

Abstract

A field experiment has been carried out with the specific objective in mind to determine the value of von Kármán's constant in atmospheric boundary layer flow, and also to investigate its possible dependence on the surface Rossby number Ro0. Data from three field measurement campaigns at Marsta, Sweden, were used in the analysis. Depending on the ground cover: deep snow (40 cm), plowed field or 15–20 cm high wheat crop the surface roughness in the three campaigns was respectively: 1 mm, 7.5 mm and 24 mm. The corresponding range in Ro0 is roughly 2.5×106−6.5×107.

In the experiment a turbulence instrument was used (the MIUU instrument) that has been carefully examined for aerodynamic error effects and duly corrected. Measurements of turbulent fluxes made with this instrument at ca. 2 and 6 m above the surface were used, together with wind profile measurements. Data from the measurements with the turbulence instruments were also used to correct the cup anemometers for overspeeding (found to be 5%).

In all, 16 hours of measurements were used for the analysis. These runs have been selected on the basis of stringent criteria on fetch requirements and minimum wind-speed required. The runs represent near neutral or slightly stable conditions (−0.04≤z/L<0.1). The quantity studied is ϕ′m=(0.4/k)ϕ(z/L)=0.4/k(∂u¯/∂zkz/u*, evaluated at z=2 m but with u* and L extrapolated to z=0 m.

The analysis gives as a result that k=0.40±0.01, with no evidence of a variation with the surface Rossby number within the range of Ro0-values encountered (2.5×106−6.5×107). This finding is in agreement with recent laboratory studies by Purtell et al. (1981), which indicate that k is independent of Reynolds number and equal to 0.41. As a by-product the constant B in the relation ϕm=1+Bz/L is determined to be 4.0 within the limited stability range encountered.

Save