Numerical investigation of two-phase secondary Kelvin-Helmholtz instability

Instability of the interface between two immiscible fluids representing the so-called Kelvin-Helmholtz instability problem is studied using smoothed particle hydrodynamics method. Interfacial tension is included, and the fluids are assumed to be inviscid. The time evolution of interfaces is obtained for two low Richardson numbers Ri = 0.01 and Ri = 0.1 while Bond number varies between zero and infinity. This study focuses on the effect of Bond and Richardson numbers on secondary instability of a two-dimensional shear layer. A brief theoretical discussion is given concerning the linear early time regime followed by numerical investigation of the growth of secondary waves on the main billow. Results show that for Ri = 0.01, at all Bond numbers, secondary instabilities start in the early times after a perturbation is imposed, but they grow only for Bond numbers greater than 1. For Ri = 0.1, however, secondary instabilities appear only at Bond numbers greater than 10. Finally, based on numerical simulations and using an energy budget analysis involving interfacial potential energy, a quantitative measure is given for the intensity of secondary instabilities using interfacial surface area.