The influence of ambient stratification on the river plume dynamics is studied using the Regional Ocean Modeling System (ROMS). The shelf flow is thermally stratified and retains a 15-m deep upper mixed layer. A buoyant inflow into the model domain is systematically varied so that both surface-advected and bottom-advected buoyant plumes are formed. The resulting buoyant plumes are compared with the corresponding numerical solutions when the ambient shelf flow is not stratified. Surface-advected plumes spread on top of the thermocline and are not affected by the ambient stratification. Bottom-advected plumes on the other hand interact with the ambient stratification by deepening the thermocline which in some cases renders the buoyancy current unstable. Bottom-advected plumes under stratified conditions exhibit the formation of a frontal disturbance at an earlier stage downstream of the anticyclonic bulge, with more eddies developing later along the density front. These eddies grow rapidly in both offshore and downstream directions and propagate with the buoyant coastal current. In an extreme case, they spread thrice the offshore extension of the plume in the corresponding nonstratified case. More eddies develop either when the inflow salinity anomaly is smaller or when the stratification is stronger. Eddies form later, grow at a slower rate and are less developed offshore with a gentler bottom slope. Frontal eddies triggered by the ambient stratification reduce (up to 35%) the downstream and enhance the offshore freshwater fluxes compared to the corresponding nonstratified case. Energy conversion diagnostics indicate that both baroclinic and barotropic instabilities contribute to the formation of frontal eddies, with baroclinic instability playing the leading role.