The growth rate of the turbulent magnetic Rayleigh-Taylor instability

The Rayleigh-Taylor instability is strongly modified in the presence of a vertical mean magnetic

field. Perturbations are firstly stretched in the vertical direction with no mixing due to the inhibition

of the small scale shear instabilities. Then, smooth elongated fingers eventually break after transition

to turbulence, and a strong anisotropy persists. For increasing Alfv`en velocities, the growth rate of

the mixing zone in the fully turbulent regime is damped due to the conversion of potential energy

into turbulent magnetic energy. A new theoretical prediction for the growth rate is proposed and

assessed with high resolution direct numerical simulations of the Boussinesq-Navier-Stokes equations

under the magnetohydrodynamics approximation.