Press release from USACE
USACE permits and regulates all dams and their flow-rate on waterways in the US.
They have CONTROL of the FLOW.
I’m not sure if they control the dams that TVA controls or not - TVA has a complete river operations control apparatus for controlling river levels, generation output schedules, water spilling schedules (if any) along the Tennessee River. They do work together with USACE for dams along the Cumberland river within TVA’s service territory though.
Interesting factoid - TVA’s Kentucky dam is near the end of the Tennessee river where it dumps into the Ohio River in western Kentucky. The Core’s Barkley Dam is less than a mile away at the end of the Cumberland River where it dumps into the Ohio river. There is a canal between the two that allows transfer of water from one reservoir to the other.