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\nPoiseuille flow is studied by direct numerical simulation. Turbulence\nlifetimes, the likelihood that turbulence is sustained, is investigated for\ntransitional flows with various slip lengths. Slip surfaces decrease the\nlikelihood of sustained turbulence compared to the no-slip case, and likelihood\nis further decreased as slip length is increased. A deterministic analysis of\nthe effects of slip surfaces on transition to turbulence is performed using\nnonlinear traveling wave solutions to the Navier-Stokes equations, also known\nas exact coherent solutions. Two solution families, dubbed P3 and P4, are used\nsince their lower-branch solutions are embedded on the boundary of the basin of\nattraction of laminar and turbulent flows (Park & Graham 2015). Additionally,\nthey exhibit distinct flow structures -- the P3 and P4 are denoted as core mode\nand critical layer mode, respectively. Distinct effects of slip surfaces on the\nsolutions are observed by the skin friction evolution, linear growth rate, and\nphase-space projection of transitional trajectories. The slip surface modifies\ntransition dynamics little for the core mode, but considerably for the critical\nlayer mode. Most importantly, the slip surface promotes different transition\ndynamics -- early and bypass-like transition for the core mode and delayed and\nH-/K-type-like transition for the critical layer mode. Based on spatiotemporal\nand quadrant analyses, it is found that slip surfaces promote the prevalence of\nstrong wall-toward motions (sweep-like events) near vortex cores close to the\nchannel centre, inducing an early transition, while sustained ejection events\nare present in the region of the ${\\Lambda}$-shaped vortex cores close to the\ncritical layer, resulting in a delayed transition.\n