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Effect of compressibility on the Rayleigh–Taylor and Richtmyer–Meshkov instability induced nonlinear structure at two fluid interface

2009; American Institute of Physics; Volume: 16; Issue: 3 Linguagem: Inglês

10.1063/1.3074789

1527-2419

Mousumi Gupta, Sourav Roy, Manoranjan Khan, H. C. Pant, Susmita Sarkar, Mohit Srivastava,

Particle Dynamics in Fluid Flows

The effect of compressibility and of density variation on Rayleigh–Taylor and Richtmyer–Meshkov instability of the temporal development of two fluid interfacial structures such as bubbles and spikes have been investigated. It is seen that the velocity of the tip of the bubble or spike increases (destabilization) if the local Atwood number increases due to density variation of either of the fluids. The opposite is the result, i.e., the bubble or spike tip velocity decreases (stabilization) if the density variation leads to lowering of the value of the local Atwood number. The magnitude of stabilization or destabilization is an increasing function of the product of the wave number k and interfacial pressure p0. The effect of compressibility is quite varied. If the heavier (upper) fluid alone is incompressible (γh→∞), but the lighter fluid is compressible the growth rate is higher (destabilization) than when both the fluids are incompressible. Moreover the heavier fluid remaining incompressible the growth rate decreases (stabilization) as γl (finite) increases and ultimately tends to the incompressible limit value as γl→∞. With γl→∞ but γh finite the growth increases (destabilization) as γh increases. When both γh and γl are finite (density ρh>density ρl) the growth is reduced when γh<γl compared to that when both fluids are incompressible and enhanced when γh>γl. The set of nonlinear equations describing the dynamics of bubbles and spikes in the presence of fluid density variations are not analytically integrable in closed form. The results derived by numerical solution methods are represented and interpreted in corresponding figures.