The non-linear theory of a warped accretion disc with the beta-viscosity prescription

We study the nonlinear dynamics of a warped or twisted accretion disc, in which the viscosity coefficients are assumed to be locally proportional to the rotational velocity (beta- prescription). Using asymptotic methods for thin discs, dynamical equations of the disc are obtained in a warped spherical polar coordinates. These equations are solved by the method of the separation of the variables. This analysis constitutes an analogous study of the nonlinear theory of an alpha model warped disc which has been studied by Ogilvie (1999). We have compared our results with Ogilvie's analysis. The dynamical behaviors of these models have also been discussed. Our results show that different viscosity prescriptions and magnitudes (alpha and beta prescriptions) affect dynamics of a warped accretion disc. Therefore it can be important in determining the viscosity law even for a warped disc.