Power-law shear-thinning fluid motions induced by a translating spherical bubble with sinusoidal oscillation at a high frequency are numerically studied. We focus on reducing the time-averaged drag force
$D$ on the bubble owing to the oscillation-enhanced shear-thinning effect. Under the assumption of negligible convection, the unsteady Stokes equation is directly solved in a finite-difference manner over a wide parameter space of the dimensionless oscillation amplitude
$A$ (corresponding to the oscillatory-to-translational velocity ratio) and the power-law index
$n$ of the viscosity. The results show that, for small amplitude (
$A\ll 1$), the drag reduction ratio
$1-D/D_0$ (here,
$D_0$ is
$D$ with no oscillation) is proportional to
$A^2$. In contrast, for large amplitude (
$A \gg 1$), the drag ratio
$D/D_0$ is proportional to
$A^{n-1}$, revealing a power-law behaviour. In the case of
$A \gg 1$ for a strong shear-thinning fluid with small
$n$, the square of the vorticity over the entire domain is much smaller than that of the shear rate, and thus the bulk flow may be regarded as irrotational. To provide a fundamental perspective on the drag reduction mechanism, a theoretical model is proposed based on potential theory, and demonstrated to well capture the power-law relation between
$D/D_0$ and
$A$.