Turbulence‐driven angular momentum transport in modulated Kepler flows

The velocity fluctuations in a spherical shell arising from sinusoidal perturbations of a Keplerian shear flow with a free amplitude parameter ε 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 ε_crit ∝ 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′_ru′_ϕ〉 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^′2_ϕ 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.