The spatial-temporal multi-scale characteristics of turbulent kinetic energy and typical structures in turbulent boundary layer.

Time series of large samples of instantaneous velocity fields with a 7.26δ0.99×1.18δ0.99 size in a turbulent boundary layer have been obtained by experimental measurement using time-resolved particle image velocimetry (TRPIV) with a four-camera array. The resultant experimental Reynolds number (Reτ) is 1046. The continuous spatial wavelet transform has been employed to convert the streamwise velocity fluctuations into multi-scale components in the streamwise direction at all wall-normal positions. The distribution of turbulence kinetic energy across all spatial scales and all wall-normal positions are determined from the multi-scale wavelet coefficients. The continuous temporal wavelet transform has also been utilized to resolve the temporal series of longitudinal velocity fluctuations into multi-scale temporal components at all wall-normal positions. The use of the multi-scale wavelet coefficients delivered the turbulent kinetic energy distribution across all temporal scales and all wall-normal positions. Moreover, the distribution of multi-scale flatness factors with spatial scales and normal position, before and after removal of multi-scale coherent structures, has been calculated. The turbulent structures are detected by zero-crossing the wavelet coefficients. The conditional sampling scheme and spatial phase-locked method have been employed to establish typical multi-scale structures at different wall-normal positions. The universality of the small-scale structures has been confirmed where the associated vorticity is characterized by an alternating positive and negative quadrupole along the longitudinal direction and wall-normal direction, while the streamlines can be considered a dynamic system composed of a saddle point and focal points. The scaling exponent Ϛ(p), before and after the removal of the coherent structures, has been calculated, confirming that the multi-scale coherent structures are responsible for the anomalous scaling law. [ABSTRACT FROM AUTHOR]