Note that during the Civil War the Tennessee River was not really navigable at Muscle Shoals, Alabama (Tuscumbia on the map). Contemporary freight would be unloaded at Decatur, AL; shipped via rail to Tuscumbia, AL and loaded onto steamers downriver. The River wasn't navigable from Paducah to Knoxville until the Tennessee Valley Authority (TVA) constructed dams and locks in the 1930s / 1940s.
The USA built gunboats at Bridgeport, TN (west of Chattanooga) after the battle of Chicamauga in 1864 to patrol the upper Tennessee River.
http://www.brownwaternavy.org/tennriver.htm