Effects of Reynolds number and spatial resolution on the pressure source terms in turbulent boundary layers

TL;DR

This paper investigates how Reynolds number and spatial resolution affect pressure source terms in turbulent boundary layers, revealing their growth with Reynolds number and the impact of PIV resolution on measurement accuracy.

Contribution

It provides the first quantification of pressure source terms' variation with Reynolds number and assesses the effects of PIV spatial resolution on their estimation.

Findings

All pressure source terms increase with Reynolds number.

Non-linear turbulence-turbulence interactions grow faster than linear mean-shear terms.

Spatial resolution significantly attenuates estimated pressure source terms.

Abstract

The increase in wall-pressure fluctuations with increasing friction Reynolds number ($Re_{\tau}$) of a turbulent boundary layer (TBL) is well known in the literature. However, very few studies have investigated the $Re_{\tau}$-variation of the source terms of the pressure fluctuations, which are solely a function of the spatial velocity gradients within the TBL. This study quantifies the pressure source terms in a zero-pressure gradient TBL by utilizing a published direct numerical simulation (DNS; Sillero et al. 2013, Phys. Fluids) database across 1000 $\lesssim$ $Re_{\tau}$ $\lesssim$ 2000. It is found that the magnitude of all source terms increases with $Re_{\tau}$ across the entire TBL thickness, with the turbulence-turbulence (non-linear) interaction terms growing faster than the mean-shear (linear) source terms. Further, we use the simulation database to mimic the scenario of particle image velocimetry (PIV) experiments that are typically spatially under-resolved compared to DNS data. It is used to quantify the effect of spatial resolution on the accuracy of pressure source terms, which are estimated here for two common PIV scenarios: (i) planar PIV in the streamwise-wall-normal plane, and (ii) stereo-PIV in the spanwise-wall-normal plane of a ZPG TBL. This exercise reveals significant attenuation of all pressure source terms compared to those estimated from the original DNS, highlighting the challenges of accurately estimating these source terms in a high $Re_{\tau}$ PIV experiment.