Weakly Nonlinear Rayleigh–Taylor Instability in Incompressible Fluids with Surface Tension

A weakly nonlinear model is established for incompressible Rayleigh–Taylor instability with surface tension. The temporal evolution of a perturbed interface is explored analytically via the third-order solution. The dependence of the first three harmonics on the surface tension is discussed. The amplitudes of bubble and spike are greatly affected by surface tension. The saturation amplitude of the fundamental mode versus the Atwood number A is investigated with surface tension into consideration. The saturation amplitude decreases with increasing A. Surface tension exhibits a stabilizing phenomenon. It is shown that the asymmetrical development of the perturbed interface occurs much later for large surface tension effect.