Numerical and Experimental Analysis of the Growth of Gravitational Interfacial Instability Generated by Two Viscous Fluids of Different Densities

In the geophysical context, there are a wide variety of mechanisms which may lead to the formation of unstable density stratification, leading in turn to the development of the Rayleigh-Taylor instability and, more generally, interfacial gravity-driven instabilities, which involves moving boundaries and interfaces. The purpose of this work is to study the level set method and to apply the process to study the Rayleigh-Taylor instability experimentally and numerically. With the help of a simple, inexpensive experimental arrangement, the R-T instability has been visualized with moderate accuracy for real fluids. The same physical phenomenon has been investigated numerically to track the interface of two fluids of different densities to observe the gravitational instability with the application of level set method coupled with volume of fraction replacing the Heaviside function. Good agreement between theory and experimental results was found and growth of instability for both of the methods has been plotted. 1. Introduction The Rayleigh-Taylor instability is instability of an interface of two fluids of different densities which occurs when the interface between the two fluids is subjected to a normal pressure gradient with direction such that the pressure is higher in the light fluid than in the dense fluid. This is the case with an interstellar cloud and shock system. A similar situation occurs when gravity is acting on two fluids of different density—with the denser fluid above a fluid of lesser density—such as water balancing on light oil. Considering two completely plane-parallel layers of immiscible fluid, the heavier on top of the light one and both subject to the Earth’s gravity, the equilibrium here is unstable to certain perturbations or disturbances. An unstable disturbance will grow and direct to a release of potential energy, as the heavier material moves down under the gravitational field and the lighter material is displaced upwards. Such instability can be observed in many situations including technological applications as laser implosion of deuterium-tritium fusion targets, electromagnetic implosion of a metal liner and natural phenomena as overturn of the outer portion of the collapsed core of a massive star, and the formation of high luminosity twin-exhaust jets in rotating gas clouds in an external gravitational potential. Various numerical and experimental works have been done by many researchers concentrating on the growth of single wavelength perturbations as well as considering different wavelength modes. Sharp [1] presented some of