Stability of magnetohydrodynamic cylindrical flows: Compressible modes

The stability analysis of an ideal magnetohydrodynamic cylindrical configuration subject to compressible perturbations is carried out assuming smooth profiles for both the magnetic field and the mass flow. The adiabatic energy equation is assumed everywhere. Subsonic and transonic regimes up to flow speeds a few times the sound speed are analyzed for models with axial mass flow and for a variety of helical magnetic models. It is shown that compressibility increases the growth rates of pure ideal magnetic models while it lowers those of the Kelvin–Helmholtz instabilities. Beyond the transonic regime, the pinching mode (m=0) is stable for a range of magnetic models wider than that of the incompressible case. The case of uniform mass density is investigated more in detail but some results for models with a nonuniform mass density are also considered.