Turbulence-driven angular momentum transport in modulated Kepler flows

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.