Orthogonal wavelet multiresolution analysis of the turbulent boundary layer measured with two-dimensional time-resolved particle image velocimetry.

The turbulent boundary layer flow measured by two-dimensional time-resolved particle image velocimetry is analyzed using the discrete orthogonal wavelet method. The Reynolds number of the turbulent boundary layer based on the friction velocity is Re_{τ}=235. The flow field is decomposed into a number of wavelet levels which have different characteristic scales. The velocity statistics and coherent structures at different wavelet levels are investigated. It is found that the fluctuation intensities and their peak locations differ for varying scales. The proper orthogonal decomposition (POD) of different wavelet components reveals a cascade of scales of coherent structures, especially the small-scale ones that are usually difficult to be identified in POD modes of the undecomposed flow field. The interactions among the scales are investigated in terms of large-scale amplitude modulations of the small-scale structures. In previous studies the velocity fluctuations are separated into two parts, the large scale and the small scale, divided usually by the boundary layer thickness. In the present study, however, the scales smaller than the boundary layer thickness are further separated. Therefore, the modulation analysis is a refined investigation that differentiates the modulation effects on separated small scales. The results reveal that the modulation effects vary among the small scales.