Near-wall Behavior of a Scale Self-Recognition Mixed SGS Model

A Scale Self-Recognition Mixed SGS Model was developed in terms of GS-SGS energy transfer in homogenius isotropic turbulence by Fukushima et al. (2015). In the present research, the near-wall characteristics of the Smagorinsky coefficient, $C_S$ are investigated in terms of GS-SGS energy transfer by analyzing DNS data of turbulent channel flows at $Re_\tau =$ 400, 800 and 1270. $C_S$ is dependent on grid anisotropy, and this cause dependences of $C_S$ on $Re_\tau$. It is revealed that $C_S$ obtained directly from the DNS data is independent of $Re_\tau$ and dependent on only dimensionless wall distance, $y^+$ and filter-width to Kolmogorov scale ratio corrected by $f$, $f \cdot {\it \Delta}/ \eta$, when the grid anisotropy is isolated from $C_S$ by using the correction function $f$ proposed by Scotti et al. (1993). The contributions of Leonard, cross and Reynolds terms to total energy transfer are also independent of $Re_\tau$ and dependent on only $y^+$ and $f \cdot {\it \Delta} / \eta$ in the near-wall region. These results suggest that $C_S$ can be determined dynamically from $f \cdot {\it \Delta}/ \eta$ in the wall turbulence if $\eta$ is sufficiently predicted from the grid scale quantities.