  The velocity fluctuations in a spherical shell arising from sinusoidal
perturbations of a Keplerian shear flow with a free amplitude parameter
\epsilon are studied numerically by means of fully 3D nonlinear simulations.
The investigations are performed at high Reynolds numbers, i.e.
  3000 < Re < 5000. We find Taylor-Proudman columns of large eddies parallel to
the rotation axis for sufficiently strong perturbations. An instability sets in
at critical amplitudes with \epsilon_crit \propto Re^-1. The whole flow turns
out to be almost axisymmetric and nonturbulent exhibiting, however, a very rich
radial and latitudinal structure. The Reynolds stress <u'_r u'_\phi> is
positive in the entire computational domain, from its Gaussian radial profile a
positive viscosity-alpha of about 10^-4 is derived. The kinetic energy of the
turbulent state is dominated by the azimuthal component <u_\phi'^2> whereas the
other components are smaller by two orders of magnitude. Our simulations
reveal, however, that these structures disappear as soon as the perturbations
are switched off. We did not find an ``effective'' perturbation whose amplitude
is such that the disturbance is sustained for large times (cf. Dauchot &
Daviaud 1995) which is due to the effective violation of the Rayleigh stability
criterion. The fluctuations rapidly smooth the original profile towards to pure
Kepler flow which, therefore, proves to be stable in that sense.
