  Marginal stability arguments are used to describe the rotation-number
dependence of torque in Taylor-Couette (TC) flow for radius ratios $\eta \geq
0.9$ and shear Reynolds number $Re_S=2\times 10^4$. With an approximate
representation of the mean profile by piecewise linear functions, characterized
by the boundary-layer thicknesses at the inner and outer cylinder and the
angular momentum in the center, profiles and torques are extracted from the
requirement that the boundary layers represent marginally stable TC subsystems
and that the torque at the inner and outer cylinder coincide. This model then
explains the broad shoulder in the torque as a function of rotation number near
$R_\Omega\approx 0.2$. For rotation numbers $R_\Omega < 0.07$ the TC stability
conditions predict boundary layers in which shear Reynolds numbers are very
large. Assuming that the TC instability is bypassed by some shear instability,
a second maximum in torque appears, in very good agreement with numerical
simulations. The results show that, despite the shortcomings of marginal
stability theory in other cases, it can explain quantitatively the
non-monotonic torque variation with rotation number for both the broad maximum
as well as the narrow maximum.

Fluid Dynamics