Multi-scale wake structures around the dune

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The three-dimensional wake structures behind a barchan dune model are investigated by the high-speed particle image velocimetry (PIV) at the Reynolds number of 5530. The measured velocity fields are first evaluated by time-averaged flow patterns and power spectra analysis. Then the one-dimensional orthogonal wavelet analysis is applied to reveal multi-scale turbulent structures and their corresponding second order statistics in the dune wake. The instantaneous multi-scale structures suggest that the large-scale structure is responsible for the formation of separation region. The intermediate-scale structure tends to be more active at the boundary of separation region, which may be due to the secondary vortex movement caused by the interactions between the wake and main flow. The appearance of small-scale vortices at the downstream of separation region indicates the breakdown process of large-scale vortices. The Reynolds stress and kinetic energy distribution suggest that the large-scale structures dominate the generation of turbulence in the dune wake. The lower kinetic energy contained in intermediate- and small- scale structures is considered to be related to smaller-scale interactions that reflect energy cascading phenomenon. The Reynolds shear stresses distributions suggest that the intermediate-scale structures also make significance in the separated boundary layer. As for small-scale structure, it is worthy to note that a region of high Reynolds shear stresses with an opposite sign is observed around the dune crest. The cross-correlation function of multi-scale structures suggest the quasi-periodicity of large-scale structure. The intermediate-scale structures also show a certain periodicity, however, such structures tend to be more unstable and the strength of them reduces as they travel downstream. When decreasing to small-scale, the vortical structures decays quickly at the downstream with larger convective velocity. This may indicate the breakdown process of large-scale vortices and the quick dissipation of small-scale vortices.