  For wall turbulence, there has been predicted a range of streamwise
wavenumbers $k_x$ such that the spectral density of streamwise velocity
fluctuations is proportional to $k_x^{-1}$. The existence or nonexistence of
this $k_x^{-1}$ law is examined here. We observe the atmospheric surface layer
over several months, select suitable data, and use them to synthesize the
energy spectrum that would represent wall turbulence at a very high Reynolds
number. The result is not consistent with the $k_x^{-1}$ law. It is rather
consistent with a recent correction to the prediction of a model of
energy-containing eddies that are attached to the wall. The reason for these
findings is discussed mathematically.
