Complex but coherent motions form and rapidly evolve within wall-bounded turbulent flows. Research over the past two decades broadly indicates that the momentum transported across the flow largely derives from the dynamics of these coherent motions. The associated spatial organization, and its inherent connection to the dynamics, motivates the present research on streamline curvature and torsion. All the present results have been calculated and compared using the existing direct numerical simulation databases for boundary layers and channel flows. Here we have investigated the statistical properties of the local curvature $\left(\kappa \right)$ and torsion $\left(\tau \right)$ of streamlines for the considered wall-bounded flows. The computation of $\kappa$ (deviation from a straight line-bending) and $\tau$ (out of plane motion-twisting) uses the local construction of the Frenet-Serret coordinate frame. The analysis shows that the statistics of these geometrical properties change significantly with wall-normal position. Even though the mean wall-normal velocity is zero (e.g., for channel flow), the wall-normal curvature component shows a notable positive peak close to the wall. The correlation coefficient and the conditional average of the wall-normal velocity corresponding to the wall-normal curvature exhibit an anticorrelation between them. The probability density function of the curvatures have been calculated across the flow and compared with the ${\kappa }^{-4}$ scaling proposed by Schaefer [J. Turbul., N28 (2012)] for both the total and fluctuating field. Although in isotropic turbulence this scaling of curvature pertains to scales that are near to and smaller than the Kolmogorov scale $\left(\eta \right)$, in wall-bounded turbulence we find the onset of this scaling to occur at slightly larger length scales of $\approx 10\eta$. In fact, the start of this scaling with wall distance coincides with the three-dimensionalization of the vorticity field and agrees with the stagnation point structure in the inertial domain observed by Dallas et al., [Phys. Rev. E 80, 046306 (2009)]. In this region, the mean radius of curvature scales like the Taylor microscale. The standard deviation of torsion exhibits a decreasing trend with distance from the wall. The torsion to curvature intensity ratio reveals that the out of plane motion of the streamlines exceeds in-plane bending. The joint pdf of curvature and velocity magnitude supports the notion that large curvature values correspond to the region near a stagnation point. Furthermore, the joint pdf results between curvature components provides information about the orientation of the streamlines at different wall-normal locations.

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• Boundary layers
• Structure & turbulence of boundary layers
• Turbulence