The response of a turbulent accretion disc to an imposed epicyclic shearing motion

We excite an epicyclic motion, the amplitude of which depends on the vertical position, z, in a simulation of a turbulent accretion disc. An epicyclic motion of this kind may be caused by a warping of the disc. By studying how the epicyclic motion decays, we can obtain information about the interaction between the warp and the disc turbulence. A high-amplitude epicyclic motion decays first by exciting inertial waves through a parametric instability, but its subsequent exponential damping may be reproduced by a turbulent viscosity. We estimate the effective viscosity parameter, αv, pertaining to such a vertical shear. We also gain new information on the properties of the disc turbulence in general, and measure the usual viscosity parameter, αh, pertaining to a horizontal (Keplerian) shear. We find that, as is often assumed in theoretical studies, αv is approximately equal to αh and both are much less than unity, for the field strengths achieved in our local box calculations of turbulence. In view of the smallness (∼0.01) of αv and αh we conclude that for βpgaspmag∼10 the time-scale for diffusion or damping of a warp is much shorter than the usual viscous time-scale. Finally, we review the astrophysical implications.