The inviscid two-dimensional Rayleigh–Taylor (RT) instability provides an excellent springboard into the mathematical study of stability because of the simple nature of the base state. This is the equilibrium state that exists before any perturbation is added to the system, and is described by the mean velocity field formula_1 where the gravitational field is formula_2 An interface at formula_3 separates the fluids of densities formula_4 in the upper region, and formula_5 in the lower region. In this section it is shown that when the heavy fluid sits on top, the growth of a small perturbation at the interface is exponential, and takes place at the rate