The observed relation between the Kolmogorov and von Karman constants in the surface boundary layer

In steady, neutrally-stratified flow over uniform terrain, the Kolmogorov constant for the one-dimensional spectrum in the inertial subrange (α ₁) and the von Karman constant of the logarithmic profile (k) are shown to be related by $$\alpha _1 k^{{4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-\nulldelimiterspace} 3}} = \left {\frac{{\sum \phi }}{{0.555}}} \right]\left {\frac{{nz}}{{\bar U_z }}} \right]^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} \left {\frac{{\ln z_2 /z_1 }}{{\bar U_2 - \bar U_1 }}} \right]^2 \simeq 0.136,$$ , where the numerical value results from field measurements recorded in near-ideal conditions. This experimentally-observed Kolmogorov-von Karman ‘K-von K’ product is close to the value designated by a one-dimensional equivalent of the theoretical relation previously given by Roth (1970). More-over, it is in remarkably close agreement with new values of both constants independently proposed in recent years.