Attached flow structure and streamwise energy spectra in a turbulent boundary layer

Abstract

On the basis of (i) Particle Image Velocimetry data of a Turbulent Boundary Layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum $E_{11}(k_x)$ in a wavenumber range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy model's prediction of these spectra, at least at the Reynolds numbers $R{e}_{\tau }$ considered here which are between $10^3$ and $10^4$. Instead, we find $E_{11}(k_x)\sim k_x^{-1-p}$ where $p$ varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent $p$ characterises the turbulence levels inside wall-attached streaky structures conditional on the length of these structures.