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Gaseous jets injected into water are found in a variety of engineering applications, and the flow is essentially unsteady and turbulent. Additionally, the high water-to-gas density ratio can result in complicated flow structures; hence, It is important to investigate their flow structures to predict the dynamical behaviors effectively. Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) is utilized in this study to elucidate the multiphase interactions in gaseous jets injected into water under the framework of the Navier-Stokes flow computations. The highlighted phenomena of the jet transportation can be observed by the LCS method, including expansion, bulge, necking/breaking, and back-attack. Besides, the observation of the LCS reveals that the back-attack stage is caused due to the injected gas has difficulties approaching the downstream region after the necking/breaking. The results indicate that the FTLE field has the potential to identify the structures of multiphase flows, and the LCS can capture the interface/barrier or the vortex/circulation region

Lagrangian-based investigation of gaseous jets injected into water by finite-time Lyapunov exponents