Wall effects on pressure fluctuations in turbulent channel flow

Abstract

The purpose of the present paper is to study the influence of wall-echo on pressure fluctuations $p^{\prime }$, and on statistical correlations containing $p^{\prime }$, {\em viz} redistribution ${\varphi }_{ij}$, pressure diffusion $d_{ij}^{(p)}$, and velocity/pressure-gradient ${\Pi }_{ij}$. We extend the usual analysis of turbulent correlations containing pressure fluctuations in wall-bounded \tsc{dns} computations [Kim J.: {\em J. Fluid Mech.} {\bf 205} (1989) 421--451], separating $p^{\prime }$ not only into rapid $p_{(\mathrm{r})}^{\prime }$ and slow $p_{(\mathrm{s})}^{\prime }$ parts [Chou P.Y.: {\em Quart. Appl. Math.} {\bf 3} (1945) 38--54], but further into volume ($p_{(\mathrm{r};\mathfrak{V})}^{\prime }$ and $p_{(\mathrm{s};\mathfrak{V})}^{\prime }$) and surface (wall-echo; $p_{(\mathrm{r};w)}^{\prime }$ and $p_{(\mathrm{s};w)}^{\prime }$) terms. An algorithm, based on a Green's function approach, is developed to compute the above splittings for various correlations containing pressure fluctuations (redistribution, pressure diffusion, velocity/pressure-gradient), in fully developed turbulent plane channel flow. This exact analysis confirms previous results based on a method-of-images approximation [Manceau R., Wang M., Laurence D.: {\em J. Fluid Mech.} {\bf 438} (2001) 307--338] showing that, at the wall, $p_{(\mathfrak{V})}^{\prime }$ and $p_{(w)}^{\prime }$ are usually of the same sign and approximately equal. The above results are then used to study the contribution of each mechanism on the pressure correlations in low Reynolds-number plane channel flow, and to discuss standard second-moment-closure modelling practices.

References in corpus (1)

• Tensorial representations of Reynolds-stress pressure-strain redistribution

Cited by in corpus (7)

• Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow
• On the wavenumber-frequency spectra of the wall pressure fluctuations in turbulent channel flow
• Analysis of wall-pressure fluctuation sources from DNS of turbulent channel flow
• Hybrid low-diffusion approximate Riemann solvers for Reynolds-stress transport
• The dissipation tensor ${\epsilon }_{ij}$ in wall turbulence
• Reynolds-stress model prediction of 3-D duct flows
• Further analysis of the budgets of the dissipation tensor ${\epsilon }_{ij}$ in turbulent plane channel flow