Shear instabilities in stellar objects: linear stability and non-linear evolution

Witzke, V. (2017). Shear instabilities in stellar objects: linear stability and non-linear evolution. (Unpublished Doctoral thesis, City, University of London)

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Abstract

Shear flows have a significant impact on the dynamics in various astrophysical objects, including accretion discs and stellar interiors. Due to observational limitations the complex dynamics in stellar interiors that result in turbulent motions, mixing processes, and magnetic field generation, are not entirely understood. It is therefore necessary to investigate the inevitable small-scale dynamics via numerical calculations. In particular a thin region with strong shear at the base of the convection zone in the Sun, the tachocline, is believed to play an important role in the Sun's interior dynamics and magnetic field generation. Velocity measurements suggest a stable tachocline. However, helioseismology can only provide large-scale time-averaged measurements, so small scale turbulent motions can still be present. Therefore, studying the stability of shear flows and their non-linear evolution in a fully compressible polytropic atmosphere provides a fundamental understanding of potential motion in stellar interiors and is the main focus of this thesis.

To commence the investigations a linear stability analysis of a stratified system in a two-dimensional Cartesian geometry is performed to study the effect of compressibility and thermal diffusivity on the stability threshold. In addition, this first investigation provides a reference for subsequent non-linear calculations. Focusing on a local model of unstable shear flows, direct numerical calculations are used to first compare numerical forcing methods to sustain a shear flow against viscous dissipation; and then to study the effect of key parameters on the saturated quasi-steady regime. Finally, magnetic fields are included and the full set of MHD equations is solved to study a potential kinematic dynamo in shear-driven turbulence.

Item Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/18239

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