Nonlinear Evolution of the Magnetohydrodynamic Rayleigh-Taylor Instability

TL;DR

This study investigates how magnetic fields influence the nonlinear development of Rayleigh-Taylor instability through 3D MHD simulations, revealing that magnetic tension suppresses small-scale mixing and leads to anisotropic structures.

Contribution

The paper presents new insights into the nonlinear evolution of magnetic Rayleigh-Taylor instability, highlighting the effects of magnetic tension on fluid mixing and structure formation.

Findings

Weak magnetic fields reduce fluid mixing and increase bubble displacement.

Strong fields produce anisotropic ropes and filaments, affecting instability morphology.

Flow along magnetic field lines leads to large-scale bubble formation at late times.

Abstract

We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability using three-dimensional MHD simulations. We consider the idealized case of two inviscid, perfectly conducting fluids of constant density separated by a contact discontinuity perpendicular to the effective gravity g, with a uniform magnetic field B parallel to the interface. Modes parallel to the field with wavelengths smaller than l_c = [B B/(d_h - d_l) g] are suppressed (where d_h and d_l are the densities of the heavy and light fluids respectively), whereas modes perpendicular to B are unaffected. We study strong fields with l_c varying between 0.01 and 0.36 of the horizontal extent of the computational domain. Even a weak field produces tension forces on small scales that are significant enough to reduce shear (as measured by the distribution of the amplitude of vorticity), which in turn reduces the mixing between fluids, and increases the rate at which bubbles and finger are displaced from the interface compared to the purely hydrodynamic case. For strong fields, the highly anisotropic nature of unstable modes produces ropes and filaments. However, at late time flow along field lines produces large scale bubbles. The kinetic and magnetic energies transverse to gravity remain in rough equipartition and increase as t^4 at early times. The growth deviates from this form once the magnetic energy in the vertical field becomes larger than the energy in the initial field. We comment on the implications of our results to Z-pinch experiments, and a variety of astrophysical systems.