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

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, A, 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{1.5Lambda} 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 x 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.