This paper presents a new generation of fast-running physics-based models to predict the wake of a semi-infinite wind farm, extending infinitely in the lateral direction but with finite size in the streamwise direction. The assumption of a semi-infinite wind farm enables concurrent solving of the laterally averaged momentum equations in both streamwise and spanwise directions. The developed model captures important physical phenomena such as vertical top-down transport of energy into the farm, variable wake recovery rate due to the farm-generated turbulence and also wake deflection due to turbine yaw misalignment and Coriolis force. Of special note is the model's capability to predict and shed light on the counteracting effect of Coriolis force causing wake deflections in both positive and negative directions. Moreover, the impact of wind farm layout configuration on the flow distribution is modelled through a parameter called the local deficit coefficient. Model predictions were validated against large-eddy simulations extending up to 45 km downstream of wind farms. Detailed analyses were performed to study the impacts of various factors such as incoming turbulence, wind farm size, inter-turbine spacing and wind farm layout on the farm wake.