The Influence of Viscosity on the Growth Rate of Rayleigh–Taylor Instability

Abstract

Nowadays, studying of hydrodynamic instabilities such as Rayleigh–Taylor instability, Richtmyer–Meshkov instability and Kelvin–Helmholtz instability is of great importance to scientists. These instabilities have plenty of applications in fluid mechanics, meteorology, astronomy and inertial confinement fusion (ICF). They play an important role in many physical phenomena. These instabilities are considered as negative factors in fusion reactions and play a significant role in decreasing the rate of ICF reactions. Among hydrodynamic instabilities, Rayleigh–Taylor instability is of particular importance. Different factors affect the growth rate of this instability. One of them is the viscosity effect of fluid molecules that reduces the growth rate of this instability and increases the rate of ICF reactions. In this research, which is a new idea and has not been presented or published anywhere up to now, the mass and the linear momentum conservation equations, known as Euler equations, are solved analytically by considering the viscosity effect of fluid molecules. In this way, by using boundary conditions and solving nonlinear equations, the growth rate of Rayleigh–Taylor instability as a function of the perturbation wave number is obtained at the interface of two fluids with different densities. This quantity is an important criterion for measuring the growth of fluid disturbances.