LAUSR

For wall turbulence, a range of streamwise wavenumbers kx has been predicted such that the spectral density of streamwise velocity fluctuations is proportional to kx−1. The existence or nonexistence of this kx−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 kx−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.For wall turbulence, a range of streamwise wavenumbers kx has been predicted such that the spectral density of streamwise velocity fluctuations is proportional to kx−1. The existence or nonexistence of this kx−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 kx−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.