Modeling the wall-normal velocity spectra in channel flow

Abstract

A model is proposed for the wall-normal Reynolds stress and its one-dimensional spectrum in channel flows. The model is tested for friction Reynolds numbers from 550 to 5200. The formulation for the stress is a simple modification of the one devised for boundary layers by Kunkel & Marusic (J. Fluid Mech. 548, 2006), and holds for $y/δ< 0.75$. The model for the spectrum holds for all wall distances. It is constructed in wavenumber space, and comprises two principal contributions to the spectrum: energy-containing motions and viscous-dominated motions. It is in accord with the attached eddy model where that applies, and the viscous contribution scales on the Kolmogorov length and velocity. Its extension to boundary layers, with no change to the constants, appears promising, including at Reynolds numbers well above those of the channel data.