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 $t>\mathrm{}{t}^{*}$ is given.

• Received 26 September 1972

DOI:https://doi.org/10.1103/PhysRevLett.29.1429