Bubble columns, where the liquid is in the continuous phase and the gas phase is on the form of dispersed bubbles, are widely utilised in many industrial applications. When designing these bubble columns it is important to be able to predict the conditions that mark the transition from homogeneous (bubbly) to heterogeneous (churn-turbulent) flow. The transition is a function of many variables, including: liquid and gas superficial velocities, bubble diameter, and liquid and gas physical properties. Linear stability analysis (LSA) has been successfully applied by many researchers to determine the gas volume fraction at which the instability takes place; and correspondingly a one dimensional stability factor, f(1), has been proposed (see for example Joshi et al. (2001)). Briefly, the LSA analysis utilises the velocity fluctuations of both the dispersed and continuous phases associated with the specific energy dissipation rate of the two phase mixture. Typically, the specific energy dissipation rate is correlated with the density of the bed. The previous analysis, however, does not consider the energy input which associated with the turbulence intensity (velocity fluctuations) of the incoming liquid stream. Usually, this component can be ignored in sparged bubble columns because its magnitude is relatively small and it also decays in the axial direction. In plunging liquid jet bubble columns the liquid is introduced as a high speed jet that entrains gas which is then broken into fine bubbles in the Mixing Zone. The bubby mixture then passes into the Two Phase Flow Zone where instabilities can be generated. The Mixing Zone is a region of high energy dissipation resulting in relatively large liquid velocity fluctuations, which can directly influence the instability of the Two Phase Flow Zone. In this study the existing linear stability analysis is modified to include the influence of inlet liquid velocity fluctuations on the stability parameter, f(1). The modified theory is applied to the previous work of Evans (1990) for a plunging liquid jet bubble column to determine the critical gas volume fraction at which transition takes place in the Two Phase Flow Zone. In order to apply the model, drift-flux analysis has been used to obtain bubble diameter as a function of gas and liquid superficial velocities, and computational fluid dynamics has been utilised to quantify the velocity fluctuations of the liquid exiting the Mixing Zone. (C) 2016 Elsevier Ltd. All rights reserved.