Elliptic Feature of Coherent Fine Scale Eddies in Turbulent Channel Flows

Direct numerical simulations (DNS) of turbulent channel flows up to $Re_{\tau}=1270$ are performed to investigate an elliptic feature and strain rate field on cross sections of coherent fine scale eddies (CFSEs) in wall turbulence. From DNS results, the CFSEs are educed and the strain rate field around the eddy is analyzed statistically. The principal strain rates (i.e. eigenvalues of the strain rate tensor) at the CFSE centers are scaled by the Kolmogorov length $\eta$ and velocity $U_k$. The most expected maximum (stretching) and minimum (compressing) eigenvalues at the CFSE centers are independent of the Reynolds number in each $y^+$ region (i. e. near-wall, logarithmic and wake regions). The elliptic feature of the CFSE is observed in the distribution of phase-averaged azimuthal velocity on a plane perpendicular to the rotating axis of the CFSE $(\omega_c)$. Except near the wall, phase-averaged maximum $(\gamma^{\ast}/\gamma_c^{\ast})$ and minimum $(\alpha^{\ast}/\alpha_c^{\ast})$ an eigenvalues show maxima on the major axis around the CFSE and minima on the minor axis near the CFSE center. This results in high energy dissipation rate around the CFSE.