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.

中文翻译：

---

无粘性圆柱界面的 Rayleigh-Taylor 和 Kelvin-Helmholtz 机制的时间不稳定性特征

使用线性时间理论检查无粘性、不可压缩和不混溶圆柱界面的稳定性特征。圆柱界面受到两种不稳定机制的影响，即瑞利-泰勒 (R-T) 和开尔文-亥姆霍兹 (K-H) 不稳定性。研究了无界液体介质中的空心射流在表面张力存在下 R-T 和 K-H 的联合作用并进行了报道。问题包括在轴向（K-H 机制）和径向（R-T 机制）上的运动使界面不稳定。不稳定行为由几个操作参数描述，即邦德数 (Bo)、韦伯数 (We) 和阿特伍德数 (A)。在这里，邦德数归因于 R-T 不稳定性，而韦伯数归因于 K-H 不稳定性。时间分析表明，邦德数在决定主要生长速率、最不稳定轴波数和截止轴波数方面起着重要作用。此外，还通过无量纲能量预算论证表明，即使径向运动中的少量能量也会导致与初级雾化相关的最不稳定波数显着增加。