Bernoulli and flow in a flooding river

[Spacedad2]

Does the top of a flowing river curve convex because of Bernoulli's Principle?
I was looking at a picture of a flooding river on Google Earth, and noticed that most of the debris was concentrated in a line down the middle of the river, corresponding to the area of most rapid flow. I know that floating objects tend to float on the highest level of water they can find, and conjectured that the fastest flow must then also have the highest surface. This opened up thinking about Bernoulli's Principle in fast flowing rivers in general.
Rocks and sand along the bottom of a river must be getting pushed into the area of fastest flow, and held there, by the higher pressure of the slower flows around the sides.
Rivers carve new channels during floods, because a small new channel would have a faster flow than the main channel, and suck(er, have more stuff pushed into it) by Bernoulli's Principle, scouring the sides of the new channel more and more.
People getting sucked into and caught by a riptide must actually be being pushed into it, and kept in it, by the higher pressures of the comparatively still waters on either side of a riptide. Same with people caught in a flooding river. Boaters often get caught in "hydraulics" below dams or obstructions, and held there, unable to break out into the river flow around them.
The question is, does the pressure of the slower water along the edges of a rushing river push enough water into the fast current to push up the surface of the river so it is convex in cross section, rather than more or less flat?
There is a river near me that has a concrete box utility duct of some sort that is square in cross section, and it crosses the river as nearly level as I can tell. I used a 6 foot bubble level and a laser pointer. During the last flood, the water in the center of the river piled up in waves against the duct in the center of the river in waves several feet high, whereas the still water at the edges of the river were only an inch or two high along the sides of the duct. I suppose the rushing water in the center of the river could have built up the waves. I took pictures at the time, but I guess I would have to have a circumstance where the water on either side of the river was definitely lower than the bottom of the duct, while the middle of the river was in contact with the bottom of the duct in order to clearly prove the evidence.

 

[Studiot]

During the last flood, the water in the center of the river piled up in waves against the duct in the center of the river in waves several feet high,

Interesting question. And well done for a bit of practical experimentation/measurement to test your ideas.

That's true physics.

The surface of flowing surface water, and even the world ocean, is far from 'flat'.
In many cases it is this deviation from flatness that provides the pressure head for the water to flow at all.
For instance any obstruction sticking up into the flow such as a weir dam or log causes an upstream 'backwater curve' which provides this.
Note that this refers to the longitudinal section; you were talking about the cross section.

A differential head of several feet would certainly lead to sideways flow.

But there are other considerations.

Bernouilli relates to laminar flow and does not take channel boundary friction into account.

Your river in spate will be in turbulent flow, so some (much) of the energy is in rotational motion.
I think the centreline waves are more likely to be the result of obstructions.

 

[Spacedad2]

Additional information is that a wave train develops during large flows of rivers, downriver from large chutes where most of the water is directed over rapids or falls. So there is something going on that makes the surface of the water mound up due to something other than obstructions. The water doesn't spread out due to its weight immediately below a falls, but somehow is forced together in the area of greatest flow, in standing waves that sometimes reach 6 or 8 feet high, and repeat a dozen times or so in the line of greatest flow, for hundreds of feet downstream from the falls. Bernoulli again, I suspect, but something else, too.

 

[Andy Resnick]

I was looking at a picture of a flooding river on Google Earth, and noticed that most of the debris was concentrated in a line down the middle of the river, corresponding to the area of most rapid flow.

Interesting observation- I'm not sure what the mechanism is. For example, blood cells tend to move to the center of the blood flow becasue blood is shear thinning:

http://www.thefreelibrary.com/Flow+characteristics+of+blood+in+microchannel-a0216041292

But I wonder if your observation is related to Taylor dispersion: surely, gravity will dominate over any Bernoulli effect in a river.

 

[Spacedad2]

I doubt Taylor dispersion enters into it. You might want to rethink how powerful Bernoulli's effect really is. The pressure transverse to the flow is reduced in direct relation to the increased dynamic pressure in the direction of flow. In the case of a stream in middle of a river, the center flow can be going 10 mph, while the eddy nearby is essentially still, or even going upstream. There would also be some momentum effects, as the water on either side is drawn toward the center, which would cause it to mound up in the center. I think that is what causes the wave trains, and possible the as-yet-unproven curved top of the river.
I'm also beginning to think that is what a tornado is -- the center vacuum is essentially a full air drain going straight up, as a monolithic bulge of warm moist air gets organized as a single mass and starts going straight up, condensing moisture, which heats the air, which causes it to rise into cooler air, which condenses more moisture, and the mass can't cool fast enough as it continues to be warmer than the air around it, for the entire 50,000 feet into the stratosphere, sucking a column of air from directly below it. As the drain sucks air into it, like a bathtub drain, it gathers oblique momentum from the air drawn to it, which begins to spin as it gets close to the column of almost complete vacuum between the cloud bottoms and the ground.