Rayleigh-Taylor instability in magnetohydrodynamics with finite resistivity in a horizontal magnetic field

Recent studies have revealed the significant influence of finite resistivity on high-energy-density plasmas, contrary to the previous findings of Jukes [J. Fluid Mech. 16, 177 (1963)]. This paper reexamines Jukes' theory in the context of magneto-Rayleigh-Taylor instability in magnetohydrodynamics with finite resistivity represented by eta. The inadequacy of Jukes' approach due to an erroneous boundary condition is demonstrated, and it is shown that although the theory provides some physical insights, it fails to capture crucial features. The dispersion relation proposed in this study highlights that larger growth rates tend to diffuse the magnetic field rapidly, negating its suppressive effect. Moreover, the Atwood number has a significant influence on the growth-rate curves' shape, which differs from those of viscous or elastic flows and ideal magnetohydrodynamics. Additionally, long wavelengths grow proportionally to eta 1/3, while alpha indicating growth rates behaves classically when the magnetic field is entirely diffused.