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

## TL;DR

This study uses advanced velocimetry data and mathematical modeling to analyze the energy spectra in turbulent boundary layers, revealing deviations from classical models and linking spectral scaling to wall-attached eddy structures.

## Contribution

It demonstrates that the streamwise energy spectrum scaling is influenced by wall-attached eddies but does not follow the traditional Townsend-Perry model at certain Reynolds numbers.

## Key findings

- Energy spectrum scales as $k_{x}^{-1-p}$ with $p$ varying with wall distance.
- Spectral scaling deviates from Townsend-Perry model predictions.
- Turbulence levels inside wall-attached streaks depend on their length.

## 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 $Re_{\tau}$ 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.