Self-similarity and growth of non-linear magnetic Rayleigh–Taylor instability — Role of the magnetic field strength

The non-linear regime of the magnetic Rayleigh–Taylor instability (MRTI) has been studied in the context of several laboratory and astrophysical systems. Yet, several fundamental aspects remain unclear. One of them is the self-similar evolution of the instability. Studies have assumed that non-linear MRTI has a self-similar, quadratic growth similar to hydrodynamic (HD) RTI. However, neither self-similarity nor quadratic growth has been proved analytically. Furthermore, an explicit understanding of the factors that control the growth of non-linear instability remains unclear. Magnetic fields are known to play a crucial role in the evolution of the instability. Yet, a systematic study discussing how the magnetic field influences the instability growth is missing. These issues were addressed by performing an analytical and numerical study of the MRTI with a uniform magnetic field. Our study reveals that the imposed magnetic field does not conform to the HD self-similar evolution. However, the influence of the imposed magnetic field decays with time ($t$) as $1/t$ relative to the other non-linear terms, making the MRTI conform to the HD self-similarity. Thus, the HD RTI self-similar scaling becomes relevant to MRTI at late times, when nonlinear dynamics dominate. Based on energy conservation, an equation for the mixing layer height ($h$) is derived, which demonstrates the quadratic growth of $h$ in time. This gave insight into various factors that could influence the non-linear growth of the instability. By studying MRTI at different magnetic field strengths, we demonstrate the role of magnetic field strength on the nonlinear growth of MRTI. Thus, the current study analytically and numerically proves the role of magnetic fields on the evolution of MRTI.