The U.S. Army Corps of Engineers Hydrologic Engineering Center (HEC) has developed the River Analysis System (RAS) that allows users “to perform one-dimensional steady flow, unsteady flow, sediment transport/mobile bed computations and water temperature modeling" at selected locales within a river's basin. In addition, with the recently introduced RAS Mapper module, users can also develop flood inundation maps. Although there are very specific data requirements, the software is free and continues to be supported and upgraded by the HEC which has been in operation since 1964. Go here to find out more about HEC-RAS.
By using a supporting piece of software, HEC-GeoRAS, an ArcGIS interface can be used to prepare data for HEC RAS import. To find out more about this capability, go here.Comment: Thanks goes out to Teri Alberico of the U.S. Army Corps of Engineers for passing along information on this software.