Quasi-self-similarity of the horizontal magnetic Rayleigh–Taylor instability

An imposed constant magnetic field parallel to the interface in the Rayleigh–Taylor framework strongly modifies the dynamics of the flow. The growth rate of the turbulent mixing layer is almost doubled compared with the purely hydrodynamic case, mainly due to a strong reduction of small-scale mixing. Indeed, magnetic tension inhibits the small-scale perturbations from developing, which in turn creates a strong anisotropy with structures elongated in the field direction. Two theoretical predictions for the asymptotic state of the magnetic Rayleigh–Taylor instability (MRTI) are put forward. First, considering the large-scale dynamics, an upper bound for the mixing layer growth rate is obtained. Second, the phenomenology is embedded in a buoyancy–drag equation from which an analytical relation between the growth rate, mixing, anisotropy and induced magnetic fields is derived. Both predictions are successfully assessed with high resolution direct numerical simulations of the Boussinesq–Navier–Stokes equations under the magnetohydrodynamics approximation. These predictions characterize the quasi-self-similar state of the MRTI driven by strong magnetic fields.