Evolution of nonlinear interfacial structure induced by combined effect of Rayleigh–Taylor and Kelvin–Helmholtz instability

The nonlinear evolution of two fluid interfacial structures such as bubbles and spikes arising due to the combined action of Rayleigh–Taylor and Kelvin–Helmholtz instability is investigated. Using Layzerʹs model analytic expressions for the asymptotic value of the combined growth rate are obtained in both cases for spikes and bubbles. However, if the overlying fluid is of lower density the interface perturbation behaves in different ways. Depending on the magnitude of the velocity shear associated with Kelvin–Helmholtz instability both the bubble and spike amplitude may simultaneously grow monotonically (instability) or oscillate with time.