Generalized Warped Disk Equations

The manner in which warps in accretion disks evolve depends on the magnitude of the viscosity. For small viscosity (α < H/R), the warp evolves in a wave-like manner; for large viscosity, H/R < α ≪ 1, it evolves diffusively. Here, α is the viscosity parameter and H/R is the disk aspect ratio. Currently there is no simple set of equations that describes the evolution in both regimes. In this paper, we describe a possible solution to this problem and introduce a set of one-dimensional equations that describe the evolution of a warped disk that are applicable in both high- A nd low-viscosity regimes for arbitrary tilts, but small warps.