The velocity fluctuations in a spherical shell arising from sinusoidal pert
urbations of a Keplerian shear flow with a free amplitude parameter epsilon
are studied numerically by means of fully 3D nonlinear simulations. The in
vestigations are performed at high Reynolds numbers, i.e. 3000 < Re < 5000.
We find Taylor-Proudman columns of large eddies parallel to the rotation a
xis for sufficiently strong perturbations. An instability sets in at critic
al amplitudes with epsilon (crit) alpha Re-1. The whole flow turns out to b
e almost axisymmetric and nonturbulent exhibiting, however, a very rich rad
ial and latitudinal structure. The Reynolds stress (u ' (r)u ' (phi)) is po
sitive 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 ' (2)(phi
)) whereas the other components are smaller by two orders of magnitude. Our
simulations reveal, however, that these structures disappear as soon as th
e perturbations are switched off. We did not find an "effective" perturbati
on whose amplitude is such that the disturbance is sustained for large time
s (cf. Dauchot & Daviaud 1995) which is due to the effective violation of t
he Rayleigh stability criterion. The fluctuations rapidly smooth the origin
al profile towards to pure Kepler flow which, therefore, proves to be stabl
e in that sense.