Inferring the Magnetic Field from the Rayleigh–Taylor Instability

Abstract

By extending the potential approach of Layzer and Goncharov to the magnetohydrodynamics equations, we find the nonlinear solutions to the single-mode Rayleigh–Taylor instability subjected to uniform magnetic fields at various inclinations. This allows us to derive the analytical prediction of the terminal bubble and spike velocities at arbitrary Atwood numbers, which are assessed against various 2D and 3D direct numerical simulations. Contrary to the linear phase, where the magnetic field inhibits or delays the instability, the growth rate may be enhanced in the nonlinear regime, exhibiting velocities faster than the Alfvén speed. This sheds light on the importance of the nondimensional number expressing the competition between the magnetic and buoyancy effects. Conversely, we show how the orientation and the intensity of the magnetic field can be simply inferred from these solutions.

Turbulent mixing in the vertical magnetic Rayleigh–Taylor instability

“…Dimensional analysis indicates that two regimes are possible for the mixing layer: either or . Consistent with the previous discussion, the former corresponds to the transient regime of rapid growth with : structures are rapidly stretched without mixing and grow at a constant velocity (Gréa & Briard 2023), whereas the latter, which is the standard self-similar regime of the RTI (Youngs 1994), is recovered after transition to turbulence and corresponds to . The turbulent mixing layer growth rate, modified by the presence of induced magnetic energy, is thoroughly analysed later in § 6.…”

“…This prediction for the growth rate, which relies on the turbulent properties of the flow, was successfully compared with high-resolution DNS. Moreover, in a companion paper (Gréa & Briard 2023), we have determined the terminal velocity of rising bubbles in the potential regime of rapid growth, thus extended the theory of Goncharov (2002) for the MRTI with an inclined .…”