Comparing the magnetic Rayleigh-Taylor instability dynamics in two- and three-dimensions

TL;DR

This study evaluates how magnetic Rayleigh-Taylor instability (MRTI) dynamics differ between two and three dimensions under varying magnetic field strengths. Using direct numerical simulations of incompressible, non-ideal MRTI with Dedalus, the authors compare 2D and 3D behavior across $B_0=1\%B_c$ to $15\%B_c$, examining mixing, energy flow, dissipation, anisotropy, and nonlinear growth. Key findings show that 3D MRTI supports undular, interchange, and mixed modes, yielding enhanced small-scale mixing and smoother mixing-layer profiles, while 2D is dominated by undular/interchange modes with larger-scale, more dispersed plumes; energy partitioning and dissipation differ substantially, with 3D displaying higher dissipation and stronger anisotropy, yet similar magnetic-to-kinetic conversion rates across dimensions. Overall, 2D MRTI cannot reliably capture 3D mixing or turbulence-driven energy dynamics, though reconnection-related energy transfer is comparably represented, underscoring the necessity of 3D modeling for magnetized MRTI.

Abstract

The magnetic Rayleigh-Taylor instability (MRTI) governs plasma mixing and transport in a wide range of astrophysical and laboratory systems. Owing to computational constraints, MRTI is often studied using two-dimensional (2D) simulations, but the extent to which 2D captures the true three-dimensional (3D) dynamics remains unclear. In this work, we perform direct numerical simulations of non-ideal, incompressible MRTI in both 2D and 3D, systematically varying the magnetic field strength from weakly to strongly magnetized regimes. We find that the 3D system exhibits richer mode interactions due to the coexistence of interchange, undular, and mixed modes structures that are inherently absent in 2D. The mixing layer in 3D has enhanced small-scale mixing and reduced fluid dispersion compared to 2D, which is characterized by large-scale plumes. Energy diagnostics reveal that the gravitational potential energy released is higher in 2D, primarily because of inefficient mixing and significant fluid dispersion. In contrast, 3D systems display greater energy dissipation and anisotropy, driven by small-scale vortical motions. The non-linear growth of the instability increases monotonically with magnetic field strength in 3D but shows a non-monotonic trend in 2D. Despite these broad differences, the rate of magnetic-to-kinetic energy conversion remains remarkably similar across dimensions, indicating that 2D simulations can meaningfully capture reconnection-driven processes but not the full turbulent evolution. Overall, our results demonstrate that 2D MRTI simulations cannot reliably represent 3D mixing, energy dynamics, or nonlinear growth, highlighting the fundamental importance of three-dimensionality in magnetized plasma instabilities.

Figures (20)

• Figure 1.1: Figure showing the initial configuration (a), and evolution (b, c, d) of magnetic Rayleigh-Taylor instability mixing layer through the density contours (2D slice at mid $y$-plane) at different time instants $t {=} 2.0,$$t {=} 4.80,$$t {=} 6.80$(from left to right). The snapshots correspond to $B_0 = 5\% B_c$ case. The red lines mark the boundaries of the mixing layer. The dashed dotted black line is the center line $z {=} 0$. The distance between the red lines is the height of the mixing layer.
• Figure 2.1: Power spectrum of 2D (blue) and 3D (red) perturbations. The dashed line is the power spectrum with a similar amplitude to 2D.
• Figure 3.1: (left) Temporal variation of volume averaged root mean square velocity ($u_{rms} (k_x, k_y)$), $y-$averaged $u_{rms}$ ($\langle u_{rms} \rangle_y (k_x, 0)$), and $x-$averaged $u_{rms}$ ($\langle u_{rms} \rangle_x (0, k_y)$) for $B_0 = 5\% B_c$. (centre, right) Power spectrum of $\langle u_{rms} \rangle_y (k_x, 0)$ and $\langle u_{rms} \rangle_x (0, k_y)$ for a magnetic field strength case of $B_0 = 5\% B_c$ at time $t = 0.2$ (centre), $t = 2$ (right) . $k$ can be $k_x$ or $k_y$ depending on the term being plotted.
• Figure 3.2: Instantaneous density contours of MRTI at two different magnetic field strengths: (left)$B_0 = 5\% B_c$; (right)$B_0 = 15\% B_c$. Both the contours are plotted at the same time instant $t = 7$.
• Figure 3.3: Comparison of mixing layer between 2D MRTI (top panel), mid-$y$ plane of 3D MRTI (middle panel), and mid-$x$ plane of 3D MRTI (bottom panel) through density contours at time $t = 6$. The left, centre and right columns show density contours at magnetic field strength $B_0 = 1\% B_c, 5\% B_c, 15\% B_c$ (right).