Nonlinear Kelvin-Helmholtz instability in hydromagnetics

Nonlinear Kelvin-Helmholtz instability for an incompressible plasma under the influence of gravity is investigated theoretically, using the method of multiple time-scales. The effect of nonlinearity is to reduce the growth rate for the linear instability and to narrow the unstable wavenumber domain. There are two cases, in one of which the effect is strong and in the other slight. The difference between these cases is studied.