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Modeling roughness effects in turbulent boundary layers by elliptic relaxation

The modeling of roughness effects in turbulent boundary layers (TBLs) is considered using the elliptic relaxation method of Durbin (1993), which takes into account non-local, wall-blocking effects. His approach considers a term, analogous to energy redistribution, that combines the effects of the near-wall velocity-pressure gradient correlation and the anisotropic dissipation rate and, by extension, the near-wall stress anisotropy and the non-local pressure-strain effects. An extensive experimental data-set comprising smoothwall and various rough-wall TBLs over distributed three-dimensional roughness (George 2005) is used to quantify this term and its response to roughness. Further, this data-set is used to estimate appropriate length and time scales for rough-wall, which are used to modify the elliptic relaxation in the v − f model framework. A priori testing of eddy viscosity using the data confirms that wall-normal stress (v) is a more appropriate velocity scale than turbulence kinetic energy in rough-wall computations.