  Experimental and numerical evidence is reviewed for the existence of a
Stewartson layer in spherical Couette flow at small Ekman and Rossby numbers
($\Ek \lsim 10^{-3}$, $\Ro \lsim 10^{-2}$), the relevant hydrodynamic regime in
the superfluid outer core of a neutron star. Numerical simulations of a
superfluid Stewartson layer are presented for the first time, showing how the
layer is disrupted by nonaxisymmetric instabilities. The unstable ranges of
$\Ek$ and $\Ro$ are compared with estimates of these quantities in radio
pulsars that exhibit glitches. It is found that glitching pulsars lie on the
stable side of the instability boundary, allowing differential rotation to
build up before a glitch.
