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

H. Mouri; T. Morinaga; S. Haginoya

doi:10.1063/1.5063545

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arXiv · 1902.07445

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

H. Mouri·T. Morinaga·S. Haginoya

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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.

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H. Mouri, T. Morinaga, S. Haginoya. 2019-02-20. Unlikely existence of $k_x^{-1}$ spectral law in wall turbulence: an observation of the atmospheric surface layer. https://doi.org/10.1063/1.5063545

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