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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
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