Opposing roles of shear-thinning on successive instabilities in Taylor–Couette flow

The intrinsic effect of shear-thinning on successive instabilities in narrow-gap Taylor–Couette flow is investigated using direct numerical simulation (DNS) with axially periodic boundary conditions, thereby eliminating endwall effects. The Carreau model is employed with three shear-thinning indices ( n equals 0.52 n = 0.52 $n = 0.52$ , 0.62 0.62 $0.62$ , 0.68 0.68 $0.68$ ), matching the experimental parameters of Cagney and Balabani ( Phys. Fluids , 2019, vol. 31, p. 053102). Shear-thinning exerts opposing influences on the two instabilities. For the primary transition from circular Couette flow to Taylor vortex flow, enhanced shear-thinning (decreasing n n $n$ ) is destabilising, with the critical Reynolds number italic Re Subscript c comma 1 Re c , 1 $\textit{Re}_{c,1}$ decreasing from 101 101 $101$ to 94 94 $94$ . In contrast, the secondary transition to wavy vortex flow is strongly stabilised, with italic Re Subscript c comma 2 Re c , 2 $\textit{Re}_{c,2}$ increasing from