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 (

,

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

115 115 $115$

to

142 142 $142$

over the same range of

n n $n$

. This opposing behaviour arises from a competition between two consequences of radial viscosity variation: the reduced viscosity near the inner wall promotes centrifugal disturbances (destabilising), while the elevated viscosity in the bulk gap damps inter-vortex oscillations (stabilising). Comparison with the non-monotonic experimental measurements of Cagney and Balabani ( Phys. Fluids , 2019, vol. 31, p. 053102) shows that the observed discrepancies originate from endwall-induced wavelength constraints and vortex drift rather than intrinsic rheological effects. These results establish the intrinsic bifurcation structure of shear-thinning Taylor–Couette flow in the narrow-gap configuration and clarify the distinct roles of rheology and confinement in successive flow transitions.