Topology of fine-scale motions in turbulent channel flow

Abstract

An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

Universality and scaling phenomenology of small-scale turbulence in wall-bounded flows

“…It can be classified into four different quadrants in the Q-R plane. 20,21 The flow patterns in Figure 3 mainly fall into two categories: stable focus/stretching, and unstable node/saddle/saddle, as confirmed by the joint pdf of Q-R in Figure 5. The contour lines exhibit the expected teardrop shape for both TCF and TBL, a typical feature of small-scale turbulence in many different types of flows.…”

“…Figure 2 presents the pdf of the cosine of the angle θ between λ 2 and ω, and between λ 1 and the wall-normal y direction, for TCF at Re τ ≈ 550 in four different regions: viscous sublayer, buffer layer, log layer, and wake region. It can be seen that the profiles for the alignment between λ 2 and ω, shown in 21 In the viscous sublayer λ 2 and ω are almost perfectly aligned as for a shear layer. The alignment between ω and the spanwise direction (z), and between λ 2 and z very near the wall was confirmed by previous work 18 and the current one (not shown here), respectively.…”

“…The direction of ω at different points in a flow field is different, but it is often aligned with λ 2 , as shown by many studies. 4,6,12,21 If the flow field around each point is mapped along the local λ 1 , λ 2 , λ 3 directions, a local flow field is obtained as it is viewed from an observer aligned with the local eigenframe. We may expect to see some common features associated with the local strain field and it is interesting to investigate their statistical structures both qualitatively and quantitatively.…”

“…Chong et al 20 proposed a topology classification for three-dimensional flow fields using tensor invariants P, Q, R, in which four different regions were categorized in the Q-R space (P = 0 for incompressible flow). Blackburn et al 21 studied these fine-scale motions in TCF and showed that the joint probability-density function (pdf) of Q-R has a teardrop shape further away from the wall, and confirmed the alignment of the vorticity vector and the intermediate eigenvector of the strain-rate tensor. In addition to the kinematics of the flow, the dynamics of turbulence flow topology was also studied.…”

Energy transfer, pressure tensor, and heating of kinetic plasma

“…It is therefore expected that strain rate is not correlated with rotation rate. In hydrodynamic turbulence away from walls [67,68], the joint PDF of Q D versus Q ω is spread very broadly.…”