Direct numerical simulation of turbulent, generalized Couette-Poiseuille flow

We present direct numerical simulation (DNS) and modelling of incompressible, turbulent, generalized Couette-Poiseuille flow. A particular example is specified by spherical coordinates (Re, θ, φ), where Re = 6000 is a global Reynolds number, φ denotes the angle between the moving plate, velocity-difference vector and the volume-flow vector and tan θ specifies the ratio of the mean volume-flow speed to the plate speed. The limits φ → 0◦ and φ → 90◦ give alignment and orthogonality, respectively, while θ → 0◦, θ → 90◦ correspond respectively to pure Couette flow in the x direction and pure Poiseuille flow at angle φ to the x axis. Competition between the Couette-flow shear and the forced volume flow produces a mean-velocity profile with directional twist between the confining walls. Resultant mean-speed profiles relative to each wall generally show a log-like region. An empirical flow model is constructed based on component log and log-wake velocity profiles relative to the two walls. This gives predictions of four independent components of shear stress and also mean-velocity profiles as functions of (Re, θ, φ). The model captures DNS results including the mean-flow twist. Premultiplied energy spectra are obtained for symmetric flows with φ = 90◦. With increasing θ, the energy peak gradually moves in the direction of increasing kx and decreasing kz. Rotation of the energy spectrum produced by the faster moving velocity near the wall is also observed. Rapid weakening of a spike maxima in the Couette-type flow regime indicates attenuation of large-scale roll structures, which is also shown in the Q-criterion visualization of a three-dimensional time-averaged flow. © The Author(s), 2024. Published by Cambridge University Press.