Mathematical modelling of two layer shallow water flow with incline and uneven bottom

This study aims to construct mathematical model of two layer shallow water flow based on physical phenomenon. The proposed model is with attention to incline and uneven bottom, usually is chosen as function of space b(x). The result is the governing equation of each layer consist of mass continuity and momentum equations. The layers of the model are determined by the density of the fluid. The first layer is water exposed to sunshine which the temperature is higher than the second layer. The difference of density between the first and the second layer results the difference of gravity force which in the second layer we use reduced gravity force (gravity force decreases due to density ratio).