The paper studies one-way and two-way coupling interactions between the liquid turbulence and bubbles' presence in bubbly jets. One-way coupling focuses on jet with low void fraction in which the bubbles have no significant effect on the hydrodynamic liquid fields in comparison to the single-phase jet. It sets out to model the interfacial momentum transfer identifying the turbulent contribution and its effect on the bubbles' dynamics and phase distribution. Two-way coupling considers jets with high void fractions where the liquid turbulence is altered by the bubbles which in turn influence the interfacial momentum transfers. This paper aims to improve the two-fluid model closures by implementing in computational fluid dynamics code a three-equation turbulence model and new interfacial momentum transfer closures. A benchmark of turbulence models combined with different interfacial exchange modeling is achieved to highlight the strong couplings between the interfacial forces, the phase distribution and the hydrodynamic fields of both phases.