  In this article the stability loss of the Hartmann flow are investigated by
applying the equations for disturbances. The velocity and electric potential
quasi-static MHD model is used. The equations allow us to calculate
time-dependent disturbance fields using a base flow and an initial disturbance.
Two type of initial perturbations are considered: the eigenfunction of the
linearized MHD equations and a fluid injection into the flow. These two
approaches lead to identical stability results. However, we found a significant
difference in the practical implementation of the two approaches. Dealing with
the eigenproblem of the linearized MHD system is a laborious task. In terms of
calculation costs it is equal to a series of nonlinear perturbation
simulations, and if the Hartmann number is increased, the proportion becomes
worse. The non-linear stability analysis produced by these two methods shows
that the injection technique can also be used in numerical analysis, and that
this method is less expensive in terms of calculation costs.
