Hydrodynamic stability and breakdown of the viscous regime over riblets

Abstract

The interaction of the overlying turbulent flow with a riblet surface and its impact on drag reduction are analysed. The ‘viscous regime’ of vanishing riblet spacing, in which the drag reduction produced by the riblets is proportional to their size, is reasonably well understood, but this paper focuses on the behaviour for spacingss+≃ 10–20, expressed in wall units, where the viscous regime breaks down and the reduction eventually becomes an increase. Experimental evidence suggests that the two regimes are largely independent, and, based on a re-evaluation of existing data, it is shown that the optimal rib size is collapsed best by the square root of the groove cross-section, ℓg+=Ag+1/2. The mechanism of the breakdown is investigated by systematic DNSs with increasing riblet sizes. It is found that the breakdown is caused by the appearance of long spanwise rollers belowy+≈ 20, with typical streamwise wavelengths λx+≈ 150, that develop from a two-dimensional Kelvin–Helmholtz-like instability of the mean streamwise flow, similar to those over plant canopies and porous surfaces. They account for the drag breakdown, both qualitatively and quantitatively. It is shown that a simplified linear instability model explains the scaling of the breakdown spacing with ℓg+.