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dc.contributor.authorOgilvie, Gordonen
dc.date.accessioned2018-08-23T09:26:30Z
dc.date.available2018-08-23T09:26:30Z
dc.date.issued2018-06-21en
dc.identifier.issn0035-8711
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/278986
dc.description.abstractThin 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.publisherOxford University Press
dc.titleAn affine model of the dynamics of astrophysical discsen
dc.typeArticle
prism.endingPage1759
prism.issueIdentifier2en
prism.publicationDate2018en
prism.publicationNameMonthly Notices of the Royal Astronomical Societyen
prism.startingPage1744
prism.volume477en
dc.identifier.doi10.17863/CAM.26368
dcterms.dateAccepted2018-02-23en
rioxxterms.versionofrecord10.1093/mnras/sty588en
rioxxterms.versionVoR*
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2018-06-21en
dc.contributor.orcidOgilvie, Gordon [0000-0002-7756-1944]
dc.identifier.eissn1365-2966
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idScience and Technology Facilities Council (ST/P000673/1)


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