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Scaling of the energy spectra of turbulent channels. (English) Zbl 1059.76031
Summary: The spectra and correlations of velocity fluctuations in turbulent channels, especially above the buffer layer, are analysed using new direct numerical simulations with friction Reynolds numbers up to $$Re_\tau=1900$$. It is found, and explained, that their scaling is anomalous in several respects, including a square-root behaviour of their width with respect to their length, and a velocity scaling of the largest modes with the centreline velocity $$U_c$$. It is shown that this implies a logarithmic correction to the $$k^{-1}$$ energy spectrum, and that it leads to a scaling of the total fluctuation intensities away from the wall which agrees well with the mixed scaling of D. B. de Graaff and J. K. Eaton [J. Fluid Mech. 422, 319–346 (2000; Zbl 0958.76509)] at intermediate Reynolds numbers, but which tends to a pure scaling with $$U_c$$ at very large ones.

##### MSC:
 76F55 Statistical turbulence modeling 76F65 Direct numerical and large eddy simulation of turbulence
##### Keywords:
anomalous scaling; velocity fluctuations
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