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 vertic al 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 ho w the epicyclic motion decays, we can obtain information about the interact ion between the warp and the disc turbulence. A high-amplitude epicyclic mo tion decays first by exciting inertial waves through a parametric instabili ty, but its subsequent exponential damping may be reproduced by a turbulent viscosity. We estimate the effective viscosity parameter, alpha(v), pertai ning to such a vertical shear. We also gain new information on the properti es of the disc turbulence in general, and measure the usual viscosity param eter, alpha(h), pertaining to a horizontal (Keplerian) shear. We find that, as is often assumed in theoretical studies, alpha(v) is approximately equa l to alpha(h) and both are much less than unity, for the field strengths ac hieved in our local box calculations of turbulence. In view of the smallnes s (similar to 0.01) of alpha(v) and alpha(h) we conclude that for beta = p( gas)/p(mag) similar to 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.