the river is (stacked?) the fresh water floats on top of the denser salt wate

Another great oceanography word - I'm getting the feeling you're thinking of stratified. (My brain is still fuzzy from the cold meds and I had to think for a while on that one!)

Both temperature and salinity (the salt content of the water) affect the density of the water - and that affects which water mass will be on top. Estuarine circulation describes what happens when a river empties fresh water into a salt water estuary. Basically what happens is that the fresh water "waters down" the salt water near the surface (this watering down is called entrainment, another great word). Then that whole, larger mass of lighter, less dense "fresher" water will leave the estuary on the surface. But because of conservation of mass, there will have to be an inflow near the bottom of the estuary - otherwise the estuary would drain! So you actually have an outflow of less dense water, and to balance that, an inflow of denser water. The key thing is that the volume of the outflow from the estuary is much greater than the volume of water that the river puts in, because of the entrainment.

There is also (surprise, surprise) inverse estuarine circulation, which happens when the river outflow is more dense than the water already in the estuary (this can happen with certain combinations of temperature and salinity of both waters - the most common example is the Mediterranean water entering the Atlantic Ocean). Then the river water sinks and flows along the bottom, and the inflow is on the top.

The characteristics of the Mediterranean outflow were useful during WW II. Apparently the submarine captains had to be aware of the flow in and out of the Mediterranean and they'd go to the depth where the water was going in the direction they planned to go, then cut the engines and let the current take them (so as not to be detected). Or something like that. (Anyone out there care to confirm or deny this one?)