{\bf Abstract} The steady bifurcation flows in a spherical gap
(gap ratio $\sigma=0.18$) with rotating inner and stationary outer spheres
are simulated numerically for $Re_{c_1}\leq Re\leq 1500$ by solving
the steady axisymmetric incompressible Navier--Stokes equations using a finite
difference method. The simulation shows that two stable steady flows
with 1 or 2 vortices per hemisphere exist for $775 \leq Re \leq 1220$ while
three stable steady flows with 0, 1, or 2 vortices per hemisphere
exist for $ 1220