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

Abstract

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.

arXiv comment8 pages, to appear in Physics of Fluids

References in corpus (5)

• Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau }\approx 5200$
• Probability density function of turbulent velocity fluctuation
• Two-point correlation in wall turbulence according to the attached-eddy hypothesis
• Probability density function of turbulent velocity fluctuations in rough-wall boundary layer
• Logarithmic scaling for fluctuations of a scalar concentration in wall turbulence

Cited by in corpus (3)

• Identification of the energy contributions associated with wall-attached eddies and very-large-scale motions in the near-neutral atmospheric surface layer through wind LiDAR measurements
• Logarithmic and nonlogarithmic scaling laws of two-point statistics in wall turbulence
• Momentum flux fluctuations in wall turbulence formulated along the distance from the wall