Slip boundary condition incorporating near-wall inertial effects in Taylor–Couette turbulence

Effective slip boundary conditions have proven effective in mechanistic interpretation and predictive modelling over micro-textured drag-reducing surfaces at moderate Reynolds numbers, but their accuracy deteriorates as the texture size and flow rate increase. Torque measurements and direct numerical simulations of Taylor–Couette turbulence over patterned slip surfaces show that this breakdown occurs in a large-texture, high-turbulence regime in which near-wall inertial convection is no longer negligible. Decomposition of angular-momentum transport reveals a near-wall modulated layer where convection is dominated by surface-induced secondary vortices, in contrast to the outer region where turbulent mixing and Taylor rolls govern the transport. Spectral kinetic-energy analysis further shows that spanwise heterogeneity generates wall modes at the texture wavenumber, which undergo self-interaction within the modulated layer and couple to the outer large-scale circulation through cascade-like transfer in the outer region. Motivated by these observations, the slip-only boundary model is extended by introducing an effective near-wall turbulent viscosity,

, to represent the convective correction. The resulting model links the texture parameters (texture width

w Superscript plus w + $w^+$

and solid fraction

phi Subscript s ϕ s $\phi _s$

) to the effective coefficients (wall slip

upper U Subscript s U s $U_s$

and

nu Subscript t comma italic eff ν t , eff $\nu _{t,\textit{eff}}$

), and thereby to the skin-friction coefficient

upper C Subscript f C f $C_f$

. This model captures the observed transition in effective slip scaling from a viscous-dominated regime

tilde left parenthesis w Superscript plus Baseline right parenthesis Superscript 3 divided by 4 ∼ ( w + ) 3 / 4 ${\sim}(w^+)^{3/4}$

to an inertial-affected regime

tilde left parenthesis w Superscript plus Baseline right parenthesis Superscript 1 divided by 4 ∼ ( w + ) 1 / 4 ${\sim}(w^+)^{1/4}$

, thus providing a predictive effective-boundary framework in turbulence over patterned slip surfaces.