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.

中文翻译：

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强耦合尘埃等离子体中重力驱动不稳定性的数值研究。第 1 部分。瑞利-泰勒不稳定性和浮力驱动的不稳定性

瑞利-泰勒 (RT) 和浮力驱动 (BD) 不稳定性是由密度不均匀的流体系统中的重力驱动的。本文研究了强耦合尘埃等离子体介质的这些不稳定性。该介质已在广义流体动力学 (GHD) 流体模型的框架中表示，该模型将其视为粘弹性介质。这里考虑 GHD 模型的不可压缩极限。RT 不稳定性针对与重力分层的渐进和急剧密度梯度进行了探索。通过研究在重力存在下上升气泡（局部低密度区域）和下降液滴（局部高密度区域）的演变来讨论 BD 不稳定性。由于上升的气泡和下降的水滴在空间分布上都是对称的，我们观察到一个下降的液滴过程相当于一个上升的气泡。我们还发现，随着介质耦合强度的增加，两种重力驱动的不稳定性都会受到抑制。这些观察结果已经通过分析以及二维非线性模拟得到了说明。本文的第 2 部分计划将目前对气泡和液滴的单独演化的研究扩展到它们的组合演化，以了解它们之间的相互作用。