Effect of shear flow and magnetic field on the Rayleigh–Taylor instability

Abstract

The effects of sheared equilibrium flow and magnetic field on the Rayleigh–Taylor instability (RTI) are investigated and the linear growth rate is obtained analytically in the presence of a sharp interface. It is shown that the shear flow acts as a driving force and is the dominating drive when Atwood number AT⁠, wave number k⁠, flow shear δu⁠, and gravitational acceleration g satisfy k(1−AT2)δu2∕AT⪢g⁠. As AT increases growth rate increases first and then falls down if (2kδu2)<g is satisfied, and otherwise it rises monotonically. When magnetic stabilizing effect governs, RTI only occurs in the long wave region and not only the permitted band, 0<k<gAT∕[vra2−δu2(1−AT2)]⁠, is extended but the instability is enhanced as δu increases or the reduced Alfvén speed vra decreases. For regime governed by the destabilizing effect of shear flow, growth rate increases as k and δu increase.