An alpha theory of time-dependent warped accretion discs

The non-linear fluid dynamics of a warped accretion disc was investigated i n an earlier paper by developing a theory of fully non-linear bending waves in a thin, viscous disc. That analysis is extended here to take proper acc ount of thermal and radiative effects by solving an energy equation that in cludes viscous dissipation and radiative transport. The problem is reduced to simple one-dimensional evolutionary equations for mass and angular momen tum, expressed in physical units and suitable for direct application. This result constitutes a logical generalization of the alpha theory of Shakura & Sunyaev to the case of a time-dependent warped accretion disc. The local thermal-viscous stability of such a disc is also investigated.