# Convection velocities and velocity coupling of outer-scaled wall-pressure fluctuations in canonical turbulent boundary layers

## TL;DR

This study investigates the dominant turbulent velocity contributions to outer-scaled wall-pressure fluctuations in boundary layers, revealing their location, scaling, and coherence through advanced measurements and analysis.

## Contribution

It introduces a novel microphone array measurement technique to isolate large-scale pressure contributions and quantifies their relationship with velocity fluctuations across Reynolds numbers.

## Key findings

- Outer-scaled pressure fluctuations are most correlated with velocities in the logarithmic region.
- Large-scale pressure energy scales with outer velocity and convects at approximately 0.75 times free stream velocity.
- Coherence between velocity and pressure fluctuations increases with Reynolds number.

## Abstract

This study shows that the turbulent velocities most strongly correlated with outer-scaled ($\delta$-scaled) wall-pressure fluctuations beneath a zero-pressure-gradient boundary layer reside within the logarithmic region. Even though contributions from the wake region are present, they are found to be statistically less dominant than those from the logarithmic region. The findings are based on bespoke measurements using an array of 63 microphones spanning 5$\delta$ in the streamwise direction (where $\delta$ is the boundary layer thickness), which synchronously captures space-time $p_w$ data alongside streamwise velocity fluctuations ($u$) from a single hotwire probe at the array's downstream end. The array is designed to spatially filter $p_w$ signals to uncover outer-scale contributions, by accurately resolving the large-scale portion of the frequency-wavenumber $p_w$ spectrum while avoiding aliasing of small-scale energy. This design, and its effectiveness in anti-aliasing, is validated against previously published low-Reynolds-number simulation datasets of turbulent boundary layer flow. Present experiments span a friction Reynolds number range of $1400 \lesssim Re_{\tau} \lesssim 5200$, over which the large-scale energy in the boundary layer grows significantly. This growth is reflected in both the frequency-wavenumber $p_w$ spectrum and the space-time $p_w$ correlations, both of which show scaling trends reflective of the large-scale pressure field convecting at an outer-scaled velocity of $0.75U_\infty$, where $U_\infty$ is the freestream velocity. The linear coherence between streamwise velocity and large-scale $p_w$ is directly quantified through space-time $p_w$--$u$ correlations, which show increasing magnitudes across the inner region with rising $Re_{\tau}$.