Analysis of Instability on the Boundary of the Inhomogeneous Fluids with Varying Densities in the Presence of Incident Shock

In the present study, the instability in the interface of two semi-infinite fluid layers with applying a shock is studied. To this end, the effect of various parameters such as fluid densities, velocities of fluids, and magnetic field on the instability is explored. By using the magneto-hydrodynamic equations, a general equation is developed for the evolution of perturbation amplitude near the interface. Analytical and graphical results indicate that the time dependent part of perturbation amplitude is the same for both the constant and varying density cases and the instability depends on the growth rate. Remarkably, the growth rate depends on the characteristics of the fluids and magnetic field and can be real or imaginary; hence, the stability condition is determined with respect to this parameter. Furthermore, it is shown that the spatial part of the perturbation amplitude in the constant density case, even with different densities, is symmetric and independent from the layer densities and damps exponentially in the two sides of the interface. On the other hand, it is shown that in the varying density case, the function of the spatial part of the perturbation amplitude depends on the parameters of the environment and the fluid; so the spatial part of the perturbation amplitude in the two fluid damps asymmetrically. Moreover, the results attained in the constant density case match the findings of the previous studies.