Air-entrainment from surface vortex at critical submergence for hydraulic intakes adversely affects the withdrawal efficiency and intake performance. In this study, flow at the lateral dual square bottom intake placed in a row operating under uniform approach flow is numerically simulated. The dual intakes are subjected to perpendicular approach flow making the withdrawal condition more complex. The interface of the air–water phase is tracked using the volume of fluid (VOF) model, both coupled and decoupled with the level-set method with different spatial discretization methods for identifying the best interface interpolation. This study is focused on the development of a methodology for the determination of critical submergence for dual intakes numerically. Surface vortex causing air-entrainment at lateral dual intake was identified using three distinct approaches and a novel methodology involving the use of volume fraction study combined with a swirling-strength based vortex detection mechanism is proposed to compute the critical submergence for the safe operation of the intakes. Further, the effect of intake pipe blockage on the critical submergence is studied using differential intake protrusions and identified that a differential protrusion of the downstream intake can reduce the critical submergence with an enhanced withdrawal capacity of the upstream intake. The computed critical submergence is validated using experimental results on lateral dual intakes and found to be within ±10% error. The results of this study will be helpful to practicing engineers in the rational design of hydraulic intakes for various diversion projects.