The battle Hostile_encounter was fought Hostile_encounter between the Army of the Cumberland under Maj. Gen. William Rosecrans and the Confederate Army of Tennessee under Gen. Braxton Bragg , and was named Name_conferral for Chickamauga Creek , which meanders near the battle Hostile_encounter area in northwest Georgia ( and ultimately flows Motion into the Tennessee River about 3.5 miles ( 5.6 km ) northeast of downtown Chattanooga ) .