Spanwise structure and scale growth in turbulent boundary layers

Abstract

Spanwise structure and growth mechanisms in a turbulent boundary layer are investigated experimentally. PIV measurements are obtained in the streamwise–spanwise ($x$–$z$)-plane from the buffer layer to the top of the logarithmic region at Re$_\theta = 1015$ and 7705. The dominant motions of the flow are shown to be large-scale regions of momentum deficit elongated in the streamwise direction. Throughout the logarithmic layer, the regions are consistently bordered by vortices organized in the streamwise direction, offering strong support for a vortex packet model. Additionally, evidence is presented for the existence and organization of hairpin vortices in the region $y^+ < 60$. Statistical evidence is also presented for two important aspects of the vortex packet paradigm: vortex organization in the streamwise direction, and the clear association of the hairpin signature with local minima in streamwise velocity. Several spanwise lengthscales are shown to vary linearly with distance from the wall, revealing self-similar growth of spanwise structure in an average sense. Inspection of the data, however, suggests that individual structures do not grow strictly self-similarly in time. It is proposed that additional scale growth occurs by the merging of vortex packets on an eddy-by-eddy basis via a vortex re-connection mechanism similar to that suggested by Wark & Nagib (1989). The proposed mechanism provides a link between vortex-pairing concepts and the observed coalescence of streaky low-speed regions in the inner layer.