In Chapters 1 through 9, we have been discussing waves and oscillations in diﬀerent media, both homogeneous and inhomogeneous. Also, we have discussed waves in ﬂuids and plasmas, considering the diﬀerent types of external forces such as gravity, pressure gradient, rotation, electric and magnetic ﬁelds. We have also brieﬂy discussed two ﬂuid description in plasmas. Needless to say, the complete discussion was mostly concentrated towards the linear theory. However, wherever possible, we have mentioned some nonlinear studies also. An important question that arises in dealing with the waves and oscillations is that of stability. We have derived the dispersion relation for the diﬀerent physical systems and discussed the nature of the modes of the system. The most important aspect that we have not so far addressed is the behavior of the perturbations (both small and ﬁnite). Are these perturbations stable or unstable? We shall address these questions in this chapter. However, we shall restrict ourselves only to linear stability theory and skip the nonlinear stabil-
ity aspects. That discussion is highly technical and is beyond the scope of this book.