The "river" itself has moved through the area for eons. However, like many Texas rivers, it meandered most of the time through the Trinity Basin. During the rainy seasons, water collecting from all points north widened river until it washed out the basin from up along Maple Ave. and the rock hill where the Beer Water Falls sits today [ the old Baby Doe's Ridge ] across to Colorado Blvd. on the east.
Old Sante Fe Rail line which became the North Dallas
 Toll Way
The Design District
Here you see the grid layout of old Downtown
Trinity River
Trinity River Basin
Trinity River 1900
Oak Cliff
Focus in on the part of the old Meanders that sits just above the "The" of Design District. Right there at that curve is where Oak Lawn Ave. cuts under Stemmons Frwy. They buried that portion of the Meanders under the Design District and built buildings over it. You can follow the underground stream today by observing where the concrete floors of the buildings sink.