Nonlinear threshold of two-dimensional Rayleigh-Taylor growth for incompressible liquid

Nonlinear threshold of two-dimensional Rayleigh-Taylor(RT) instability is analyzed in planar and cylindrical and spherical geometries. Density amplitude is defined relating to instable interface and formulas of nonlinear threshold values for RT instability in three kinds of geometries are given, then high-order algorithm is used to simulate two-dimensional RT instability in these geometries, and t he simulation results agree well with the formulas.