Dynamics of laminar and transitional flows over slip surfaces: effects on the laminar-turbulent separatrix

Abstract

The effect of slip surfaces on the laminar-turbulent separatrix of plane Poiseuille flow is studied by direct numerical simulation. Turbulence lifetimes, the likelihood that turbulence is sustained, is investigated for transitional flows with various slip lengths. Slip surfaces decrease the likelihood of sustained turbulence compared to the no-slip case, and likelihood is further decreased as slip length is increased. A deterministic analysis of the effects of slip surfaces on transition to turbulence is performed using nonlinear traveling wave solutions to the Navier-Stokes equations, also known as exact coherent solutions. Two solution families, dubbed P3 and P4, are used since their lower-branch solutions are embedded on the boundary of the basin of attraction of laminar and turbulent flows (Park & Graham 2015). Additionally, they exhibit distinct flow structures -- the P3 and P4 are denoted as core mode and critical layer mode, respectively. Distinct effects of slip surfaces on the solutions are observed by the skin friction evolution, linear growth rate, and phase-space projection of transitional trajectories. The slip surface modifies transition dynamics little for the core mode, but considerably for the critical layer mode. Most importantly, the slip surface promotes different transition dynamics -- early and bypass-like transition for the core mode and delayed and H-/K-type-like transition for the critical layer mode. Based on spatiotemporal and quadrant analyses, it is found that slip surfaces promote the prevalence of strong wall-toward motions (sweep-like events) near vortex cores close to the channel centre, inducing an early transition, while sustained ejection events are present in the region of the $Λ$-shaped vortex cores close to the critical layer, resulting in a delayed transition.