Tensorial representations of Reynolds-stress pressure-strain redistribution

Abstract

The purpose of the present note is to contribute in clarifying the relation between representation bases used in the closure for the redistribution (pressure-strain) tensor ${\varphi }_{ij}$, and to construct representation bases whose elements have clear physical significance. The representation of different models in the same basis is essential for comparison purposes, and the definition of the basis by physically meaningfull tensors adds insight to our understanding of closures. The rate-of-production tensor can be split into production by mean strain and production by mean rotation $P_{ij}=P_{{\bar{S}}_{ij}}+P_{{\bar{\Omega }}_{ij}}$. The classic representation basis $\mathfrak{B}[\tsr{b}, \tsrbar{S}, \tsrbarΩ]$ of homogeneous turbulence {\em [{\em eg} Ristorcelli J.R., Lumley J.L., Abid R.: {\it J. Fluid Mech.} {\bf 292} (1995) 111--152]}, constructed from the anisotropy $\tsr{b}$, the mean strain-rate $\tsrbar{S}$, and the mean rotation-rate $\tsrbarΩ$ tensors, is interpreted, in the present work, in terms of the relative contributions of the deviatoric tensors $P_{{\bar{S}}_{ij}}^{(\mathrm{dev})}:=P_{{\bar{S}}_{ij}}-\frac{2}{3}{P}_{\mathrm{k}}{\delta }_{ij}$ and $P_{{\bar{\Omega }}_{ij}}^{(\mathrm{dev})}:=P_{{\bar{\Omega }}_{ij}}$. Different alternative equivalent representation bases, explicitly using $P_{{\bar{S}}_{ij}}^{(\mathrm{dev})}$ and $P_{{\bar{\Omega }}_{ij}}$ are discussed, and the projection rules between bases are caclulated, using a matrix-based systematic procedure. An initial term-by-term {\em a priori} investigation of different second-moment closures is undertaken.

arXiv commentASME J. Appl. Mech. (in print); final version; 10 pages, 2 Figs

Cited by in corpus (6)

• Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow
• Wall effects on pressure fluctuations in 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