River plumes are low-salinity water masses formed in the upper layer of seawater when freshwater from rivers carries terrestrial substances into the ocean. River plumes can have intense material exchange and water mixing effects with seawater, exerting significant influences on the physical and chemical properties and ecological environment of coastal areas. Previous studies have shown that different estuaries are influenced by environmental factors such as wind fields, runoff and tides, forming river plumes of various shapes. Some river plumes exhibit multi-scale instabilities with mesoscale eddies at the bulge center and co-occurrence sub-mesoscale eddies at the plume front. However, these studies did not systematically summarize and generalize the universal laws of river plume instability. Therefore, based on the available worldwide satellite data, this study deeply explored the multi-scale instabilities characteristics of different river plumes from various continents around the world. We extracted the characteristics of river plumes and their related environmental parameters, introducing the BIN (Bulge Instability Number) and BIP (Baroclinic Instability Parameter) to evaluate and predict the stability state of the river plume. We obtained data such as slope, river flow, vortex radius and mixing depth through publicly available data (i.e., the GEBCO dataset, the GRDC dataset and the Copernicus). Combined with latitude, river runoff and other data, the BIN and BIP values were calculated to classify the stability of global river plume systems. This research is conducive to promoting a semi-empirical global river plume stability prediction model, providing new ideas on mesoscale-induced transport and mixing in the coastal oceans.