## An affine model of the dynamics of astrophysical discs

dc.contributor.author | Ogilvie, Gordon | en |

dc.date.accessioned | 2018-08-23T09:26:30Z | |

dc.date.available | 2018-08-23T09:26:30Z | |

dc.date.issued | 2018-06-21 | en |

dc.identifier.issn | 0035-8711 | |

dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/278986 | |

dc.description.abstract | Thin astrophysical discs are very often modelled using the equations of 2D hydrodynamics. We derive an extension of this model that describes more accurately the behaviour of a thin disc in the absence of self-gravity, magnetic fields, and complex internal motions. The ideal fluid theory is derived directly from Hamilton's Principle for a 3D fluid after making a specific approximation to the deformation gradient tensor. We express the equations in Eulerian form after projection on to a reference plane. The disc is thought of as a set of fluid columns, each of which is capable of a time-dependent affine transformation, consisting of a translation together with a linear transformation in three dimensions. Therefore, in addition to the usual 2D hydrodynamics in the reference plane, the theory allows for a deformation of the mid-plane (as occurs in warped discs) and for the internal shearing motions that accompany such deformations. It also allows for the vertical expansions driven in non-circular discs by a variation of the vertical gravitational field around the horizontal streamlines, or by a divergence of the horizontal velocity. The equations of the affine model embody conservation laws for energy and potential vorticity, even for non-planar discs.We verify that they reproduce exactly the linear theories of 3D warped and eccentric discs in a secular approximation. However, the affine model does not rely on any secular or small-amplitude assumptions and should be useful in more general circumstances. | |

dc.publisher | Oxford University Press | |

dc.title | An affine model of the dynamics of astrophysical discs | en |

dc.type | Article | |

prism.endingPage | 1759 | |

prism.issueIdentifier | 2 | en |

prism.publicationDate | 2018 | en |

prism.publicationName | Monthly Notices of the Royal Astronomical Society | en |

prism.startingPage | 1744 | |

prism.volume | 477 | en |

dc.identifier.doi | 10.17863/CAM.26368 | |

dcterms.dateAccepted | 2018-02-23 | en |

rioxxterms.versionofrecord | 10.1093/mnras/sty588 | en |

rioxxterms.version | VoR | * |

rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | en |

rioxxterms.licenseref.startdate | 2018-06-21 | en |

dc.contributor.orcid | Ogilvie, Gordon [0000-0002-7756-1944] | |

dc.identifier.eissn | 1365-2966 | |

rioxxterms.type | Journal Article/Review | en |

pubs.funder-project-id | Science and Technology Facilities Council (ST/P000673/1) |