Turbulent channel flow with large-amplitude velocity oscillations

Abstract

Measurements in turbulent channel flow with forced oscillations covering a wide range of frequencies (ω+ = 0.03–0.0005) and amplitudes (10–70% of centreline velocity) are presented and discussed. Phase averages of the velocity <u> across the flow, and of the wall shear stress <τ>, as well as the turbulent fluctuations <u′u′> and <t′t′> are obtained with LDA and hot-film techniques. The time-mean quantities, except u’2, are only slightly affected by the imposed oscillations whatever their frequency and amplitude. It is shown that the appropriate similarity parameter for the oscillating quantities ũ and ĩ is the non-dimensional Stokes length l+s (or the frequency ω+ = 2/l+2s). In the regime of high-frequency forcing (l+s < 10) the oscillating flow ũ and ĩ are governed by purely viscous shear forces although the time-mean flow is fully turbulent. This behaviour may be explained by the physical significance of l+s. At lower frequency l+s 10, the oscillating flow is influenced by the turbulence, in particular the amplitude of ĩ increases with respect to the Stokes amplitude and becomes proportional to l+s. The relative amplitude of <u′u′> and <t′t′> decreases sharply with increasing forcing frequency once l+s < 25. This decay of the turbulence response is faster for the wall shear stress. For forcing frequencies such that l+s > 12, <u′u′> and <t′t′> lag behind <u> and <τ> by respectively about 75 and 130 viscous time units. These lags decrease by a factor 2 at higher forcing frequencies. It is shown that in the log layer, the turbulence modulation diffuses away from the wall with a diffusivity equal to that of the time-mean turbulence. The imposed oscillations are felt down to the small scales of the turbulence as may be evidenced from the cyclic modulation of the Taylor microscale, the skewness and the flatness factors of δu′/δt. The modulations of the skewness and the flatness go through a maximum around l+s = 12.