Density currents formed by buoyancy discharges from rivers are numerically studied using non-dimensional two layer model including Coriolis acceleration, bottom stress, interfacial friction. Some typical numbers such as Froude number, densimetric Froude number and Kelvin number are obtained and some characteristic scales are defined as a result of non-dimensionalization of the governing equations. Besides the Coriolis effect, the configurations of bottom topography, bottom friction coefficient and interfacial friction are found to significantly affect the propagation of the warm water plume. Frontal position can fastly propagate in the case of large density difference between the two layers and small interfacial friction. Left side boundary current is easily formed under the small interfacial friction. With large Kelvin number, both right and left side boundary currents are formed. Wave-like disturbances and eddies are easily formed under the high Froude number.