# The perturbation of a turbulent boundary layer by a two-dimensional hill

## TL;DR

This study experimentally investigates how a two-dimensional hill perturbs a turbulent boundary layer, analyzing flow velocity, stress distributions, and bed instabilities using Particle Image Velocimetry in water flows.

## Contribution

It provides new experimental data on turbulent boundary layer perturbations caused by a hill, linking flow behavior to bed instabilities and validating asymptotic analyses.

## Key findings

- Flow velocities and stresses are significantly altered by the hill.
- Surface shear stress correlates with bed instabilities.
- Experimental results align with theoretical asymptotic predictions.

## Abstract

Turbulent boundary layers over flat walls in the presence of a hill are frequently found in nature and industry. Some examples are the air flows over hills and desert dunes, but also water flows over aquatic dunes inside closed conduits. The perturbation of a two-dimensional boundary layer by a hill introduces new scales in the problem, changing the way in which velocities and stresses are distributed along the flow. When in the presence of sediment transport, the stress distribution along the hill is strongly related to bed instabilities. This paper presents an experimental study on the perturbation of a fully-developed turbulent boundary layer by a two-dimensional hill. Water flows were imposed over a hill fixed on the bottom wall of a closed conduit and the flow field was measured by Particle Image Velocimetry. From the flow measurements, mean and fluctuation fields were computed. The general behaviors of velocities and stresses are compared to published asymptotic analyses and the surface shear stress is analyzed in terms of instabilities of a granular bed.