Are you building this in the middle of the river?
Build the Southern Border Fence (double fencing, set in concrete, with a 30 yard space between)
The majority of that border is a river.
Are you building this in the middle of the river?
Seems a bit lacking in planning RE that river, huh?
Give the freaking river to Mexico...for all I care.
Actually, only the Texas border is the Rio Grand...and people cross it all of the time.
I would build the fence on our side of the river, set back for major flood control issues. I believe the border probably runs down the middle, but having it on our side will suffice.
Fences can be built to handle the river...it is done all of the time.
If there are necessary entry points to the River, you treat those just like you do for border crossings.
There is no reason why that cannot, and should not be done. it will provide the same deterrence to crossers. They will have no place to go if they do succeed in swimming.