A numerical study of gravity-driven instability in strongly coupled dusty plasma. Part 1. Rayleigh–Taylor instability and buoyancy-driven instability

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Abstract
Rayleigh–Taylor (RT) and buoyancy-driven (BD) instabilities are driven by gravity in a fluid system with inhomogeneous density. The paper investigates these instabilities for a strongly coupled dusty plasma medium. This medium has been represented here in the framework of the generalized hydrodynamics (GHD) fluid model which treats it as a viscoelastic medium. The incompressible limit of the GHD model is considered here. The RT instability is explored both for gradual and sharp density gradients stratified against gravity. The BD instability is discussed by studying the evolution of a rising bubble (a localized low-density region) and a falling droplet (a localized high-density region) in the presence of gravity. Since both the rising bubble and falling droplet have symmetry in spatial distribution, we observe that a falling droplet process is equivalent to a rising bubble. We also find that both the gravity-driven instabilities get suppressed with increasing coupling strength of the medium. These observations have been illustrated analytically as well as by carrying out two-dimensional nonlinear simulations. Part 2 of this paper is planned to extend the present study of the individual evolution of a bubble and a droplet to their combined evolution in order to understand the interaction between them.

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