Compressibility effects on the Rayleigh-Taylor instability growth between immiscible fluids

Abstract

The linearized Navier-Stokes equations for a system of superposed immiscible compressible ideal fluids are analyzed. The results of the analysis reconcile the stabilizing and destabilizing effects of compressibility reported in the literature. It is shown that the growth rate $n$ obtained for an inviscid, compressible flow in an infinite domain is bounded by the growth rates obtained for the corresponding incompressible flows with uniform and exponentially varying density. As the equilibrium pressure at the interface $p_{\infty }$ increases (less compressible flow), $n$ increases towards the uniform density result, while as the ratio of specific heats $\gamma$ increases (less compressible fluid), $n$ decreases towards the exponentially varying density incompressible flow result. This remains valid in the presence of surface tension or for viscous fluids and the validity of the results is also discussed for finite size domains. The critical wavenumber imposed by the presence of surface tension is unaffected by compressibility. However, the results show that the surface tension modifies the sensitivity of the growth rate to a differential change in $\gamma$ for the lower and upper fluids. For the viscous case, the linearized equations are solved numerically for different values of $p_{\infty }$ and $\gamma$. It is found that the largest differences compared with the incompressible cases are obtained at small Atwood numbers. The most unstable mode for the compressible case is also bounded by the most unstable modes corresponding to the two limiting incompressible cases.

arXiv commentTo appear in Physics of Fluids

Cited by in corpus (13)

• Revisiting the Late-Time Growth of Single-mode Rayleigh-Taylor Instability and the Role of Vorticity
• Rayleigh-Taylor instability in partially ionized compressible plasmas: one fluid approach
• On the Rayleigh-Taylor Instability of Radio Bubbles in Galaxy Clusters
• Scale interactions and anisotropy in Rayleigh-Taylor turbulence
• Two-fluid simulations of Rayleigh-Taylor instability in a magnetized solar prominence thread. I. Effects of prominence magnetization and mass loading
• Viscous effects on the Rayleigh-Taylor instability with background temperature gradient
• A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 1: the 1-D case
• A numerical study of gravity driven instability in strongly coupled dusty plasmas.Part I: Rayleigh-Taylor instability and Buoyancy-driven instability
• Knudsen number dependence of 2D single-mode Rayleigh-Taylor fluid instabilities
• Immiscible Rayleigh-Taylor turbulence using mesoscopic lattice Boltzmann algorithms
• Magnetic Rayleigh-Taylor Instability at a Contact Discontinuity With Oblique Magnetic Field
• Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh-Taylor system
• Numerical simulations of compressible Rayleigh-Taylor turbulence in stratified fluids