15th Conference on Boundary Layer and Turbulence

9.2

On Reasons for the Observed Variation of the von Karman Constant in the Atmospheric Surface Layer

Christoph A. Vogel, NOAA/ARL/ATDD, Oak Ridge, TN; and P. Frenzen

Experimental evidence obtained in recent years indicates that the von Karman scaling factor k does not have a constant value in the atmospheric surface layer. Apparently the variation is related to changes in turbulence intensity: k seems to vary with a roughness Reynold's number Re. However, there has yet to be a plausible explanation for why such a variation should occur. The present study makes some limited illustrations of two possible causes recently proposed using data from a field experiment designed to observe fundamental characteristics of atmospheric turbulence over rougher terrain.

In a recent note, Frenzen has shown that in neutral conditions the von Karman constant can be expressed as:

\begin{displaymath}k=\frac{A \overline{U}}{z} \left[\frac{u_*^2}{\left(E^*/\alpha_1\right)}\right]^{3/2}\end{displaymath}

where U is the mean horizontal wind, u2* the momentum flux, z the height above the ground, a1 the Kolmogorov constant, and E* the spectral energy density in the inertial subrange multiplied by f+5/3 where f is frequency. A is a proportionality factor which provides a measure of the relative contribution of dissipation to the total amount of turbulence removed: specifically,

$A\equiv\epsilon/\left(\epsilon +D\right)$
where D represents the sum of the divergent turbulence and pressure transport terms in the turbulent kinetic energy equation. Thus, A is a relative measure of the "dissipation deficit" found by a number of investigators.

The relation in the equation above offers two mechanisms which could explain the apparent variation of k with Re observed in the field. An indication of the first can be seen in a comparison of spectral and cospectral analyses given by Lumley and Panofsky in their figure 5.19. The momentum flux in the numerator of the expression for k given here is systematically attenuated in the higher frequencies by the growth of the inertial subrange with increasing Re because of the inability of the isotropic portion of the turbulence field to transfer momentum. In these same conditions, the average amplitude of the inertial subrange, as expressed in the denominator of the expression above, remains unaffected. The second mechanism involves the question as to whether or not the dissipation deficit factor A remains constant with increasing Re as has been suggested. The present study examines the relative significance of these two possibilities, in so far as possible, using data obtained in the 1991 Glencoe field experiment conducted in the Hay plains of central New South Wales, Australia.

extended abstract  Extended Abstract (44K)

Session 9, Fundamental Studies of Turbulence, including advances in LES and DNS, Laboratory Studies, and Observations
Wednesday, 17 July 2002, 8:30 AM-12:30 PM

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