Rayleigh-Taylor Instability and Turbulence in the Presence of Magnetic Fields
Xin Bian, PhD Defense, Advised by Hussein Aluie
Monday, May 24, 2021
Turbulence is fluid motion that evolves and consists of fluctuations or ``eddies'' at different length-scales and time-scales, often triggered by hydrodynamic instabilities. The thesis focuses on one such instability, the Rayleigh-Taylor instability (RTI), and its transition to turbulence, which is important in many scientific and engineering fields ranging from nuclear fusion to astrophysics. In these systems, magnetic fields can play a crucial role in the evolution of the flow. We have carried out a careful and systematic study of the magnetic field influence on RTI growth, and on the energetic pathways in the ensuing turbulent flow.
In the first part of the thesis, we study the nonlinear growth of RTI in 2-dimensional (2D) and 3-dimensional (3D) configurations using high-resolution simulations. Our results show that, even at a high Atwood number, bubble re-acceleration is still possible if the large perturbation Reynolds number limit is taken first. The analysis of vorticity dynamics suggests that vorticity accumulation inside bubble tip is the key mechanism contributing to bubble re-acceleration. We then analyze the magneto-RTI (mRTI) and show how an external magnetic field affects bubble development in 2D and 3D. The external magnetic field affects drag, vortical motion, and buoyancy during the nonlinear development of mRTI. The dominant process determines whether the magnetic field suppresses or enhances mRTI development.
In the second part of the thesis, we study the energy cascade and turbulent transport coefficients in magnetohydrodynamic (MHD) turbulence using a coarse-graining approach and direct numerical simulations with grid points up to $2048^3$. Despite its complex and chaotic nature, we show that turbulence in fact leads to simplified MHD dynamics in the form of new emergent conservation laws -- the magnetic and kinetic energy budgets statistically decouple beyond a transitional ``conversion'' range, i.e., magnetic and kinetic energy each cascades conservatively. From the conservative cascades, we derive new models for the turbulent transport coefficients that are a function of scale. These transport coefficients have power-law scalings in the ``decoupled range''. Our findings have important implications in astrophysical systems and offer a guide for large eddy simulation modeling.