Geometric properties of streamlines in turbulent wall-flows
Document TypeMasters Research thesis
Access StatusOpen Access
© 2019 Rina Perven
Streamline geometry has been studied in case of turbulent wall flows. 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 derives from the dynamics underlying these coherent motions. This spatial organization, and its inherent connection to the dynamics, motivates the present research. The local streamline geometry pertaining to curvature $(\kappa)$ and torsion $(\tau)$ has apparent connection to the dynamics of the flow. The present results indicate that these geometrical properties change significantly with wall-normal position. One part of this research is thus to clarify the observed changes in the streamline geometry with the known structure and scaling behaviours of the mean momentum equation. Towards this aim, the curvature and torsion of the streamlines at each point in the volume of existing boundary layers and channel DNS has been computed. The computation of $\kappa$ and $\tau$ arise from the local construction of the Frenet-Serret coordinate frame. The present methods for estimating $\kappa$ includes components of curvature in the streamwise, wall-normal and spanwise direction. The analysis shows that 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. This arises from the strong wallward flow followed by a weak movement of the streamlines away from the wall. The correlation coefficient and the conditional average of the wall-normal velocity corresponding to the wall-normal curvature exhibit an anti-correlation between them. The probability density function of the curvatures have been calculated at some wall-normal locations of interest and compared with a scaling of the exponent of $-4$ for both total and fluctuating field. This scaling of curvature values describes the geometric features of the length scales that are smaller than the Kolmogorov scale. The onset of this scaling with wall distance has a potential connection to the three-dimensionalization of the vorticity field and the stagnation points structure in the inertial domain. In this region, the mean radius of curvature scales like Taylor microscale. The probability density functions of the wall-normal curvature show that high curvature regions similar to those in isotropic flow begin to appear outside the viscous wall layer. The standard deviation for torsion exhibits a decreasing effect with distance from the wall. The torsion to curvature ratio reveals the intensity of out of plane motion of the streamlines relative to their in-plane bending. The joint pdf of curvature with 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 reveal the orientation of the streamlines at different wall-normal locations. Overall the curvature and torsion statistics examined thus far point to intriguing correlations with the four layer structure associated with known structure of the vorticity field in turbulent wall-flows.
KeywordsWall-bounded turbulence; Streamline geometry; Curvature; Torsion; Geometric properties of streamline; Mean momentum balance layer; Wall-flow dynamics; Curvature and torsion of streamline; Geometrical properties of wall-flow; Curvature near Stagnation points; Connection of Geometry and wall-flow dynamics
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