抄録
In normal mode analysis, the unstable mode grows as an exponential function of time, and the stable mode oscillates as a trigonometric function of time. At a critical point of the relevant parameter space, the mode becomes marginally unstable. The marginally unstable mode is a degenerate mode of growing and decaying modes, as shown by Xu (2007) in the symmetric instability. In this note, we examine marginally unstable modes of gravitational, barotropic and baroclinic instabilities. As in the case of symmetric instability, the marginally unstable modes grow as a linear function of time. In the case of gravitational instability, the linear growth of the marginally unstable mode is rather trivial. On the other hand, in the cases of barotropic and baroclinic instabilities, the linear growth is not trivial, and can be qualitatively explained in terms of the PV thinking.
