Temporal instability characteristics of Rayleigh–Taylor and Kelvin–Helmholtz mechanisms of an inviscid cylindrical interface

Abstract

The stability characteristics of an inviscid, incompressible and immiscible cylindrical interface are examined using linear temporal theory. The cylindrical interface is subjected to two instability mechanisms, namely Rayleigh–Taylor (R–T) and Kelvin–Helmholtz (K–H) instabilities. The combined action of R–T and K–H in the presence of surface tension is investigated for a hollow jet in an unbounded liquid medium and reported. The problem includes the motion in an axial direction (K–H mechanism) and the radial direction (R–T mechanism) to destabilize the interface. The instability behavior is described by a few operating parameters, namely, Bond number (Bo), Weber number (We) and Atwood number (A). Here, Bond number is attributed to R–T instability whereas Weber number is attributed to K–H instability. The temporal analysis reveals that the Bond number plays a significant role in determining the dominant growth rate, most unstable axial wavenumber and cut-off axial wavenumber. Furthermore, it is also shown through dimensionless energy budget arguments, even a small amount of energy in the radial motion causes the most unstable wavenumber associated with primary atomization to increase significantly.