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For wall turbulence, there has been predicted a range of streamwisewavenumbers $k_x$ such that the spectral density of streamwise velocityfluctuations is proportional to $k_x^{-1}$. The existence or nonexistence ofthis $k_x^{-1}$ law is examined here. We observe the atmospheric surface layerover several months, select suitable data, and use them to synthesize theenergy spectrum that would represent wall turbulence at a very high Reynoldsnumber. The result is not consistent with the $k_x^{-1}$ law. It is ratherconsistent with a recent correction to the prediction of a model ofenergy-containing eddies that are attached to the wall. The reason for thesefindings is discussed mathematically.

Unlikely existence of $k_x^{-1}$ spectral law in wall turbulence: an observation of the atmospheric surface layer