Full Record

Author | Donnelly, Cara |

Title | Shearing waves and the MRI dynamo in stratified accretion discs |

URL | https://doi.org/10.17863/CAM.16134 https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.633480 |

Publication Date | 2014 |

Degree | PhD |

Degree Level | doctoral |

University/Publisher | University of Cambridge |

Abstract | Accretion discs efficiently transport angular momentum by a wide variety of as yet imperfectly understood mechanisms, with profound implications for the disc lifetime and planet formation. We discuss two different methods of angular momentum transport: first, generation of acoustic waves by mixing of inertial waves, and second, the generation of a self-sustaining magnetic field via the magnetorotational instability (MRI) which would be a source of dissipative turbulence. Previous local simulations of the MRI have shown that the dynamo changes character on addition of vertical stratification. We investigate numerically 3D hydrodynamic shearing waves with a conserved Hermitian form in an isothermal disc with vertical gravity, and describe the associated symplectic structure. We continue with a numerical investigation into the linear evolution of the MRI and the undular magnetic buoyancy instability in isolated flux regions and characterise the resultant quasi-linear EMFs as a function of height above the midplane. We combine this with an analytic description of the linear modes under an assumption of a poloidal-toroidal scale separation. Finally, we use RAMSES to perform full MHD simulations in a zero net flux shearing box, followed by spatial and a novel temporal averaging to reveal the essential structure of the dynamo. We find that inertial modes may be efficiently converted into acoustic modes for "bending waves", despite a fundamental ambiguity in the inertial mode structure. With our linear MRI and the undular magnetic buoyancy modes we find the localisation of the instability high in the atmosphere becomes determined by magnetic buoyancy rather than field strength for small enough azimuthal wavenumber, and that the critical Alfven speed below which the dynamo can operate increases with increasing distance from the midplane. We calculate analytically quasi-linear EMFs which predict both a vertical propagation of toroidal field and a method for creation of radial field. From our fully nonlinear calculations we find an electromotive force in phase with the toroidal field, which is itself 3π/2 out of phase with the radial (sheared) field at the midplane, and good agreement with our quasi-linear analytics. We have identified an efficient mechanism for generating acoustic waves in a disc. In our investigation of the accretion disc dynamo, we have reproduced analytically the EMFs calculated in our simulations, given arguments based on the phase of relevant quantities, several correlation integrals and the scalings suggested by our analytic work. Our analysis contributes significantly to an explanation for the dynamo in an accretion disc. |

Subjects/Keywords | 523.01; Protoplanetary disks ; Angular momentum ; Theory of Wave-motion ; Shear flow ; Dynamo theory (Cosmic physics) |

Rights | Full text available |

Country of Publication | uk |

Record ID | oai:ethos.bl.uk:633480 |

Other Identifiers | 10.17863/CAM.16134 |

Repository | ethos |

Date Retrieved | 2020-09-29 |

Date Indexed | 2020-10-05 |

Sample Search Hits | Sample Images | Cited Works

…1.7 Generation of acoustic waves . . . . . . .
1.8 Magnetic fields . . . . . . . . . . . . . .
1.8.1 The MRI and magnetic buoyancy
1.8.2 *Dynamo* *theory* . . . . . . . . . .
1.9 Thesis outline . . . . . . . . . . . . . . .
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…This Thesis is the result of my own work and includes nothing which
is the outcome of work done in collaboration.
Shearing Waves and the MRI *Dynamo* in
Stratified Accretion Discs
CJ Donnelly
Accretion discs efficiently transport angular momentum by a…

…waves, and second, the generation
of a self-sustaining magnetic field via the magnetorotational instability
(MRI) which would be a source of dissipative turbulence. Previous
local simulations of the MRI have shown that the *dynamo* changes…

…structure of the *dynamo*.
We find that inertial modes may be efficiently converted into acoustic modes for “bending waves”, despite a fundamental ambiguity in
the inertial mode structure. With our linear MRI and the undular
magnetic buoyancy modes we find the…

…localisation of the instability
high in the atmosphere becomes determined by magnetic buoyancy
rather than field strength for small enough azimuthal wavenumber,
and that the critical Alfven speed below which the *dynamo* can operate increases with increasing…

…our investigation of the accretion disc *dynamo*,
we have reproduced analytically the EMFs calculated in our simulations, given arguments based on the phase of relevant quantities,
several correlation integrals and the scalings suggested by our analytic…

…work. Our analysis contributes significantly to an explanation
for the *dynamo* in an accretion disc.
Contents
Contents
xi
1 Introduction
1.1 Observations . . . . . . . . . . . . . . . .
1.2 Accretion disc structure . . . . . . . . .
1.3 2D disc…

…A
3.6.2 Set Pm = 1 . . . . . . . . . . . . . . . . . . . .
3.6.3 MRI polarisation: weak field limit and kz kx
3.6.4 Undular polarisation: kx kz . . . . . . . . . .
3.6.5 Effects of Pm on the *dynamo* . . . . . . . . . . .
3.7 Limitations…