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.

目前，研究Ra​​yleigh-Taylor不稳定性、Richtmyer-Meshkov不稳定性和Kelvin-Helmholtz不稳定性等流体动力学不稳定性对科学家来说具有重要意义。这些不稳定性在流体力学、气象学、天文学和惯性约束聚变 (ICF) 中有大量应用。它们在许多物理现象中发挥着重要作用。这些不稳定性被认为是聚变反应中的负面因素，并且在降低 ICF 反应速率方面起着重要作用。在流体动力学不稳定性中，瑞利-泰勒不稳定性尤为重要。不同的因素会影响这种不稳定性的增长率。其中之一是流体分子的粘度效应，它降低了这种不稳定性的生长速率并增加了 ICF 反应的速率。在这项研究中，这是一个新想法，迄今为止尚未在任何地方提出或发表，质量和线性动量守恒方程，称为欧拉方程，是通过考虑流体分子的粘度效应来解析求解的。这样，通过使用边界条件和求解非线性方程，在两种不同密度的流体的界面处获得了瑞利-泰勒不稳定性的增长率作为摄动波数的函数。这个量是衡量流体扰动增长的重要标准。在具有不同密度的两种流体的界面处获得了作为微扰波数函数的瑞利-泰勒不稳定性的增长率。这个量是衡量流体扰动增长的重要标准。在具有不同密度的两种流体的界面处获得了作为微扰波数函数的瑞利-泰勒不稳定性的增长率。这个量是衡量流体扰动增长的重要标准。