In this project, I explore the drivers of turbulence in flow-driven disks: instabilities.
Dr. Fatima Ebrahimi and I recently submitted our first paper on the confinement mechanisms of these MHD instabilities, see it on arXiv! Another paper is going to be published soon on the comprehensive spectral and simulated stability analysis of MHD instabilities.
Continuing my work from my thesis, I extended the ideal eigenvalue analysis method to finite resistivity. This method I presented at APS-DPP 2024, where I was able to show very good match in terms of frequency, mode structure, and growth rate to initial-value simulations from NIMROD.
I used this connection to extend the work to a phase-plot, akin to that in Condensed Matter - a given phase being determined by the most unstable mode at a given set of parameters. In effect, this allows researchers to look at a given set of parameters and know what mode will be dominant, which is particularly relevant to experiments looking for these modes (i.e. PPPL’s MRI experiment).
My thesis focused on classifying the stability of disks under different resistivities, flow configurations, and global curvature. This is particularly important, as it can be used to describe drivers of increased viscosity both in astrophysical and experimental disks of this form.
This was achieved through two methods. First, I studied the stability of linear wave-like perturbations to the Magneto-Hydrodynamics (MHD) equations via spectral analysis. I then compared these (ideal) results to (non-ideal) initial-value simulations that I performed in NIMROD. In this thesis I did not include the final form for non-ideal spectral analysis, but I would later present this at APS-DPP 2024.
In effect, this work provides a template for understanding the drivers of turbulence in these types of disks by classifying the driving instability. Future work should include non-linear simulations to classify momentum transport, which can be used as a final method to confirm which mode causes increased accretion in disks of this type.
The first part of my thesis consisted of completing arrays of linear initial-value simulations via the code NIMROD, so that we could understand how resistivity affects the relative dominance of the modes.
I presented this research at my first major conference: APS DPP 2023. From this research, it was concluded that the more localized modes, (See Fig 4c,e,f) scale heavily with resistivity, whereas the global modes (see Fig 4a,b,d) scale weakly. This work would continue in my thesis where I attempted to classify this scaling with resistivity, and how the ideal dominance of the modes vary with aspect ratio and flow configuration.