Undergraduate Thesis Or Project
 

Beating Modes in Protostellar Disks

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  • Computational simulations of disks are becoming an important tool to predict the the evolution of protostars and disks to better understand the formation of planets. Past research has shown that the evolution of disks and their protostar can be altered through the interaction between gravity and hydrodynamic instabilities. We perform linear hydrodynamic simulations and analyze characteristic eigenmodes that depend on the geometry, velocity field, and star to disk mass ratio. Many modes arise when the equilibrium system is perturbed and typically the fastest growing mode will dominate the system early in the evolution of the model. On the thresholds between modal types such as Jeans-like modes, P modes and intermediate I modes we observe a phenomenon that resembles beating between two waves. We investigate this hypothesis using Fourier methods to decompose the time history of the perturbed amplitude of the eigenfunction into characteristic frequencies. Analysis shows this beating behavior can be understood as a superposition of modes across the threshold of the I- and I+ intermediate modes. I- modes are fast waves characterized by co-rotation near the inner edge of the disk, while I+ plus modes are slow waves characterized by co-rotation near the outer edge of the disk. We show the correlation between modes that arise in the numerical simulation in our Fourier analysis. We find that higher order terms in solving the fluid conservation equations are needed in linear simulations to understand this beating behavior. These terms correspond to mode coupling within the disk as shown by the finding Fourier coefficients through the evolution of the simulation. We propose a solution to the beating through modifying the linearized equations.
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