A spatiotemporal analysis is performed for an incompressible and inviscid compound jet moving in an unbounded inviscid static medium in this article. A detailed parametric study is carried out to explore the transition from absolute to convective instability for different operating conditions. The absolute and convective regions are shown through four plots: (i) inner density ratio ($Q_i$) and Weber number ($We$), (ii) outer density ratio ($Q_o$) and Weber number ($We$), (iii) surface tension ratio ($\sigma$) and Weber number ($We$) and (iv) radius ratio ($\lambda$) and Weber number ($We$). There exists a critical Weber number below which the compound jet becomes absolutely unstable and above which the compound jet becomes convectively unstable. The present results complement the existing results and give a complete theoretical understanding of the compound jets instability behavior.

本文对在无边界的无粘性静态介质中移动的不可压缩和无粘性复合射流进行了时空分析。进行了详细的参数研究，以探索不同操作条件下从绝对不稳定到对流不稳定的转变。绝对和对流区域通过四个图显示：（i）内部密度比（${问}_{\mathrm{一世}}$）和韦伯编号（$\mathrm{w\; ^}Ë$），（ii）外部密度比（${问}_{Ø}$）和韦伯编号（$\mathrm{w\; ^}Ë$），（iii）表面张力比（$\sigma$）和韦伯编号（$\mathrm{w\; ^}Ë$）和（iv）半径比（$\lambda$）和韦伯编号（$\mathrm{w\; ^}Ë$）。存在一个临界韦伯数，低于该韦伯数时，复合射流变得绝对不稳定，超过此值时，复合射流变得对流不稳定。目前的结果补充了现有的结果，并提供了对复合射流不稳定性行为的完整理论理解。