Nonlinear Evolution of the Rayleigh-Taylor Instability of a Thin Layer

An exact, closed-form, nonlinear solution is obtained for the Rayleigh-Taylor instability of a thin fluid layer. If the layer evolves from a small sinusoidal perturbation, its subsequent shape is in the form of a cycloid. The solution is good up to a time t* after which adjacent segments of the layer begin to collide with each other. A qualitative discussion of the layer dynamics for t>t* is given.