Fluctuating pressure correlations in wall turbulence

Details Fluctuating pressure correlations in wall turbulence Fluctuating pressure correlations in wall turbulence

2011-01-07

arxiv.org/abs/1101.1876v1

Physics

Fluid Dynamics

submitted for publication (62 pages, 18 Figs, 3 Tabs)

Scientific paper

The purpose of the present paper is to study the influence of wall-echo on pressure fluctuations $p'$, and on statistical correlations containing $p'$, {\em viz} redistribution $\phi_{ij}$ and pressure diffusion $d_{ij}^{(p)}$. 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 $p'$ not only into rapid $p_{(\mathrm{r})}'$ and slow $p_{(\mathrm{s})}'$ parts [Chou P.Y.: {\em Quart. Appl. Math.} {\bf 3} (1945) 38--54], but further into volume (weakly inhomogeneous; $p'_{(\mathrm{r};\mathfrak{V})}$ and $p'_{(\mathrm{s};\mathfrak{V})}$) and surface (strongly inhomogeneous wall-echo; $p'_{(\mathrm{r};w)}$ and $p'_{(\mathrm{s};w)}$) 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. The \tsc{dns} results are then used to assess several representative second-moment closures for near-wall turbulence. An extended representation basis including a tensor based on the unit vector in the dominant direction of turbulence inhomogeneity is proposed and applied in representing different models in a common framework.

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