Vortex sheet motion in incompressible Richtmyer–Meshkov and Rayleigh–Taylor instabilities with surface tension

Abstract

Effect of compressibility on the Rayleigh-Taylor and Richtmyer-Meshkov instability induced nonlinear structure at two fluid interface Phys. Plasmas 16, 032303 (2009); 10.1063/1.3074789 Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shellsMotion of a planar interface in incompressible Richtmyer-Meshkov ͑RM͒ and Rayleigh-Taylor ͑RT͒ instabilities with surface tension is investigated numerically by using the boundary integral method. It is shown that when the Atwood number is small, an interface rolls up without regularization of the interfacial velocity. A phenomenon known as "pinching" in the physics of drops is observed in the final stage of calculations at various Atwood numbers and surface tension coefficients, and it is shown that this phenomenon is caused by a vortex dipole induced on the interface. It is also shown that when the surface tension coefficient is large, finite amplitude standing wave solutions exist for the RM instability. This standing wave solution is investigated in detail by nonlinear stability analysis. When gravity is taken into account ͑RT instability͒, linearly stable but nonlinearly unstable motion can occur under a critical condition that the frequency of the linear dispersion relation in the system is equal to zero. Further, it is shown that the growth rate of bubbles and spikes under this critical motion is neither of the exponential type nor of the power law type at both the linear stage and the asymptotic stage.

Nonlinear interaction between bulk point vortices and an unstable interface with nonuniform velocity shear such as Richtmyer–Meshkov instability

“…The method presented here is also applicable to the interaction between an interface and point vortices in capillary-gravity waves, if we change the initial condition for the interface and take the surface tension effect into account. 64 Those calculations, including the ones for higher Atwood numbers, will be reported elsewhere.…”

Discrete Boltzmann modeling of Rayleigh-Taylor instability: effects of interfacial tension, viscosity and heat conductivity

“…Whereas Huang, et al showed that the growth of bubble amplitude does not always slow down with increasing interfacial tension but is promoted within a small range of interfacial tension [41]. In addition to its effect on bubble growth rate and amplitude, interfacial tension also exhibits effects such as squeezing of spikes, inhibition of interfacial coiling, induction of interfacial pinch-off to form discrete droplets, etc [42][43][44]. Capillary waves, squeezing, and rupture during the evolution of RTI are also caused by interfacial tension [45].…”

Linear and nonlinear interactions between an interface and bulk vortices in Richtmyer–Meshkov instability

“…In the current study, approximating the bulk vortices by point vortices, we investigate the nonlinear interaction between the bulk vortices and the interface using the vortex sheet model (VSM). [28][29][30][31] VSM is a powerful tool for investigating the nonlinear interfacial dynamics such as the Kelvin-Helmholtz instability, 32,33 the Rayleigh-Taylor instability, 28,[34][35][36] and RMI, 9,[28][29][30][31]37,38 in which the unstable interface is regarded as a vortex sheet without thickness. 39 In VSM, the interfacial velocity is provided as the vortex-induced velocity by the Birkhoff-Rott equation.…”