Effects of surface tension and rotation on the Rayleigh–Taylor instability

Abstract

The effects of surface tension and uniform rotation of a vertical axis are theoretically investigated for three-fluid systems. The fluids are considered to be incompressible with varying density. Numerical results were obtained for two-fluid and three-fluid systems, namely air–water, water–mercury, hexane–NaCl, NaCl–CCl₄, air–water–mercury and hexane–NaCl–CCl₄. It is found that in the case of the two-fluid systems for the values studied here, rotation has no effect on the critical value of stability. The same phenomenon holds for the three-fluid cases. For the case in which one of the surface tensions T or T′ vanishes there are always two modes. One becomes stable while the other continues to grow exponentially with time. When both surfaces have non-vanishing surface tensions, the short wavelength perturbations will become completely stabilized. In the second case irregular behaviour of the growth rate as a function of the intermediate layer d is observed. This irregular behaviour and some other important results are reported here for the first time.