Dynamics of large-scale structures in turbulent flow over a wavy wall

Abstract

We describe the dynamics of large-scale structures in a developed turbulent flow between a train of waves and a flat wall. A water channel facility, for which the wavelength, $\Lambda$, of the bottom wall equals the channel height and the wave amplitude is ten times smaller, is used. The channel is sufficiently wide so that structures of spanwise scale O$\{1.5\Lambda\}$ meander laterally. The paper dicusses the temporal behaviour and the meandering motion at a Reynolds number of 4500, defined with the half channel height and the bulk velocity. Digital particle image velocimetry is performed in a horizontal plane with a field of view of $2.6\Lambda\times 2.7\Lambda$. Ten ensembles of 90 consecutive image pairs are acquired at a rate of 15 Hz, a temporal resolution sufficient to assess how the largest flow scales evolve in time. The streamwise velocity $u(x,z,t)$ is filtered using the dominant eigenfunctions that are obtained by a proper orthogonal decomposition analysis. The very large temporal scales of the meandering motion of the O$\{1.5\Lambda\}$ structures could be followed over measurement times of up to 6 s, during which they are convected downstream by distance of 65 wavelengths. The observed coherent lengths in the streamwise direction are significantly larger than the streamwise domain extent of all large-eddy simulation and direct numerical simulation reported so far.