During SHEBA, the experiment to study the Surface Heat Budget of the Arctic Ocean, we continuously measured profiles of wind speed [U(z)], friction velocity (u_* ), and sensible heat flux with sonic anemometer/thermometers at five heights (z) on a 20-meter tower on sea ice for almost a year. We averaged the measurements hourly and thus have roughly 8000 hours of profile data. Here, we use these data to evaluate the von Kármán constant, k.

To use only the best data for this analysis, we did strict screening. We discarded any hour for which the wind may have been disturbed by the tower itself or by the structures in the surrounding ice camp. We also required that all five tower levels reported good values of the wind speed and the friction velocity. To confine our analysis to near-neutral stratification--when we can assume that the wind speed profile is semi-logarithmic--we eliminated any hour for which all five wind speeds were not at least 4 m/s (e.g., Andreas and Claffey, 1995). We then did a least-squares linear regression of U(z) versus ln(z) and further discarded any hours for which the resulting correlation coefficient was not at least 0.99. We again screened the surviving data for near-neutrality by keeping only hours for which 10/L was between -0.1 and 0.1, where L is the Obukhov length in meters.

This stringent screening reduced the original 8000 hours of data to 524 hours of near-neutral data from which we could compute k from the slope of the U(z)-versus-ln(z) fit and our measured friction velocities. The results are quite startling. k has a distinct and robust dependence on the roughness Reynolds number Re_* that is even stronger than reported by Oncley et al. (1996). (Here, Re_*=u_*z₀/n, where z₀ is the roughness length and n is the kinematic viscosity of air.) That is, k falls to values of 0.3 and smaller when Re_* is greater than 100. On the other hand, as the flow becomes aerodynamically smooth, 0.1 < Re_* < 1, k tends to become independent of Re_* and approaches the constant value of 0.436 that Zagarola and Smits (1998) found in their careful investigation of turbulent flow in an aerodynamically smooth pipe.