Incompressible Magnetohydrodynamic Kelvin–Helmholtz Instability with Continuous Profiles

Effects of a continuous magnetic field in the direction of streaming on the incompressible Kelvin–Helmholtz instability (KHI) are investigated by solving the linear ideal magnetohydrodynamic equations. It is found that the frequency of the KHI is not influenced by the magnetic field. The magnetic field strength effect decreases the linear growth of the KHI, while the magnetic field gradient scale length effect increases its linear growth. The KHI can even be completely suppressed when the magnetic field is strong enough. The linear growth rate approaches a maximum when the magnetic field gradient scale length is large enough.