Rayleigh-Taylor stability of a two-fluid system under a general rotation field

Abstract

Abstract In this paper we investigate the Rayleigh-Taylor instability of a two-fluid layer system under a general rotation field. Gravity is always perpendicular to the two horizontal layers and rotation has an arbitrary angle with respect to the vertical. It is found that, in an unstable situation, an increase in the non-dimensional density-difference increases the stable angular area of wave propagation, measured with respect to the horizontal component of rotation. However, it is found that the vertical component of rotation reduces not only this stable angular area but also the range in which the horizontal component stabilizes the system according to a previous study by Davalos-Orozco ( Fluid Dyn. Res. , 12: 243, 1993). This decrease in stable area occurs along with a decrease in the growth rate in the unstable region. Numerical analysis of the eigenvalue equation shows that the stable angular area disappears after the non-dimensional vertical component of rotation attains the value 0.33. Exact and approximate analytical expressions for the critical values are calculated to help to understand the physics of the numerical analysis.