  The difficulty of determining the slope of the famed logarithmic law in the
mean velocity profile in wall-bounded turbulent flows, the inverse of the
Karman 'constant' $\kappa$, from direct numerical simulations (DNS) is
discussed for channel flow. Unusual approaches, as well as the analysis of the
standard log-indicator function are considered and analyzed, leading to the
conclusion that a definitive determination of the channel flow $\kappa$ from
DNS with an uncertainty of, say, 2-3% will require the residue of the mean
stream-wise momentum equation in the simulations to be reduced by at least an
order of magnitude.
