Structure of turbulence in planar rough Couette flows

On roughening one of the walls in a planar Couette flow, it was reported that turbulence augments near the opposite wall [Javanappa and Narasimhamurthy, “Turbulent plane Couette flow with a roughened wall,” Phys. Rev. Fluids 6, 104609 (2021)]. The current direct numerical simulation work further explores this interesting phenomenon by investigating the flow dynamics and anisotropic nature of turbulence. For roughening, transverse square ribs are placed only on the bottom wall with streamwise pitch separations $s=5r$ and 10r, where $r=0.2h$ is the rib height and h is the channel half height. The time series of spanwise vorticity fluctuation in the case of $s=10r$ shows the presence of coherent Kelvin–Helmholtz-like structures behind the ribs. Phase analysis using Hilbert transform reveals that the flow within the cavity for the $s=5r$ case is in-phase, while a phase shift is observed for the $s=10r$ case. The visualization of enstrophy production rate (⁠$ωiSijωj$⁠) reveals that regions of intense positive ones are observed to be topologically “sheet-like,” while the regions of negative ones are found to be “spotty.” Anisotropy tensors and anisotropic invariant maps are used to explore turbulence anisotropy at both large and small scales of motion. It is observed that anisotropy is reduced in both the cases near the vicinity of roughness.