# Generalised warped disk equations

## TL;DR

This paper introduces a unified set of one-dimensional equations that describe the evolution of warped accretion disks across both low and high viscosity regimes, addressing a gap in existing models.

## Contribution

It provides a novel, simplified mathematical framework applicable to both wave-like and diffusive warp evolutions in accretion disks.

## Key findings

- The equations work for arbitrary tilts with small warps.
- They unify the description of warp evolution across viscosity regimes.
- Potential for improved modeling of accretion disk dynamics.

## Abstract

The manner in which warps in accretion disks evolve depends on the magnitude of the viscosity. For small viscosity $(\alpha < H/R)$ the warp evolves in a wave-like manner; for large viscosity $H/R<\alpha \ll 1$ it evolves diffusively. Here $\alpha$ is the viscosity parameter and $H/R$ the disk aspect ratio. Currently there is no simple set of equations which 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 and low viscosity regimes for arbitrary tilts, but small warps.