ABSTRACT
There are many situations in which a mechanical system is in equilibrium but unstable. The simplest to visualize is a ball balanced on a convex surface. A small displacement causes it to roll down the hill. The initial state is unstable. In general, any equilibrium state is unstable if a small displacement reduces the potential energy. Conservation of energy requires that the kinetic energy of its components must increase and the system moves from the equilibrium. Instabilities arise because the system is in unstable equilibrium. A small perturbation of the state leads to a decrease in potential energy of the system so that its oscillation or wave energy increases. There must be an inhomogeneity in the system so that there is available potential energy in neighbouring states of the equilibrium. There are some fluid instabilities that occur in any fluid, whether it is an Magnetohydrodynamic medium or not.
