Rayleigh–Taylor Instability with General Rotation and Surface Tension in Porous Media

The Rayleigh–Taylor instability of a heavy fluid supported by a lighter one is investigated in the presence of general rotation and surface tension through a porous medium. The density in the lower region is assumed to be a decreasing exponential function, while the density in the upper region is an increasing exponential function. The dispersion relation that defines the growth rate N for the considered system has been derived and numerically analyzed for special cases. The results show that N decreases as the vertical and horizontal components of rotation, medium porosity (ε) and viscosity increase. In the general case, only one of the critical values \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(F_{s_c})}$$\end{document} for the stability is determined.