Rayleigh-Taylor instability and the use of conformal maps for ideal fluid flow

Potential theory permits ideal fluid dynamics to be formulated in terms of boundary motion. In two dimension, the flow can then be found using conformal mapping. The evolution of some Rayleigh-Taylor instabilities is calculated well into the large amplitude nonlinear regime. The Rayleigh-Taylor calculation for Atwood ratio unity is used as a prototype for a system of theoretical and numerical techniques exploiting complex variable theory and high-order quadrature methods.