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 −1 x . The existence or nonexistence of this k −1x 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 −1 x 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.
Within wall turbulence, there is a sublayer where the mean velocity and the variance of velocity fluctuations vary logarithmically with the height from the wall. This logarithmic scaling is also known for the mean concentration of a passive scalar. By using heat as such a scalar in a laboratory experiment of a turbulent boundary layer, the existence of the logarithmic scaling is shown here for the variance of fluctuations of the scalar concentration. It is reproduced by a model of energy-containing eddies that are attached to the wall.
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