Rivers flow downhill to the sea. Does this elevation drop always take the form of a series of level changes in the form of waterfalls, rapids and other turbulent-surface situations? Or is it possible for a long section of river with a completely smooth surface to change elevation over its length? I am thinking of a wide, flat and relatively slow-moving river such as the Thames flowing through London.
My instinct tells me that the smooth surface of the river must be flat (i.e. at equipotential with the earth’s gravitational field). If I am right, the section of the river that flows into the sea (the tidal section of the river) is at sea level all the way up to the lowest weir.
As sea level changes periodically with the tides and this level change propagates upriver, will there necessarily be a wavefront or bore disrupting the smooth surface? Or can the level change continuously along the length of the river while the surface remains smooth?
I am assuming (based on my own experience with the Liffey) that when the tide is rising, the direction of flow in the river channel remains the same (the river continues to flow downstream, albeit more slowly), so the level rise comes from river water backing up, rather than actually being filled from the sea.
Coming from the other direction, if a major rainfall event in the river’s catchment area causes an increase in the volume of water flowing downstream, what effect will that have on the level in the tideway?
Put another way, the flow of water from one place to another is a result of it “trying” to be flat. Whether it is smooth or turbulent flow depends on what it is flowing over.
I don’t know if this helps, but you can think of a river like a resistor. If the current is zero, then the difference in voltage is also zero. However, if there is a current, then (assuming positive resistance), there must be some finite voltage drop.
The river is the same way. It does have resistance, from flowing across the irregular bed, viscosity, wind, etc. So if there is a positive flow then there must be a drop in potential.
A river of superfluid helium could be flat since it has no viscosity, just as a current through a superconductor will have zero voltage drop.
This doesn’t seem quite right. This is what I think the OP is getting at:
Imagine a pipe on a gentle slope, blocked at the downhill end. Fill it about half full of water. The water will sit in the pipe with a horizontal surface. Now make a small opening at the downhill end of the pipe. The water will flow down down the pipe and out of the small opening, but the surface of the water will remain horizontal.
Whereas if you make a large opening at the bottom of the pipe (open the pipe completely), and keep pouring water in at the top, then the water will move rapidly through the pipe and will not maintain a horizontal surface, the surface will be turbulent and roughly parallel to the pipe and the slope.
The OP’s question is interesting, and neither of the above pipe scenarios really correspond to he dynamics of a large slow-moving river with a smooth surface. Is the surface gently sloping with respect to the geoid? I guess it must be.
Yes this is what I understood his question to be. In your example, the water is only turbulent because of the restrictions caused by the pipe. A large smooth river is like the pipe in that it is not horizontal, but smooth because the depth and topography make it smooth.
If a river flows it must have a gradient, otherwise how is it flowing?
There must be a gradient, sure, but my first pipe scenario has water flowing down a gradient while maintaining a horizontal upper surface. I don’t disagree with your conclusion - that pipe model obviously doesn’t correspond to a steadily & continuously flowing river. I was just trying to illustrate what I thought OP was getting at.
Even if the river bottom is flat and level won’t the river flow if water is added just at one end? As said above, the river surface will try to be flat.
The equilibrium state of a large body of water is flat. But a river is not in an equilibrium state. It’s constantly gaining water at one end (or more likely, at many points along its length), and losing it at the other. In such a state, it’s perfectly possible for it to be both smooth and sloped.
The precise answer here is going to hinge on just what qualifies as the OP’s “completely smooth surface”.
Slow flow in a wide channel over a smooth hard surface might qualify. But change any of those and the smoothness of the water surface will inevitably deteriorate.
Both quite correct, of course - I think the issue with a huge slow-moving river is just that when we look at a large slow-moving things, we don’t have good intuition that they are in fact still dynamic and not in equilibrium.
This is a good point, and I’ve been thinking about what exactly I mean by a smooth surface for the purpose of this question. By “smooth surface” I mean something like that the slope of the surface is a continuous 2D function. My intention is to distinguish from stretches of river that include rapids, waterfalls, weirs, etc. Obviously it doesn’t have to be perfectly smooth (there may be surface ruffles) as long as there are no discrete changes of level.
The kind of river I am thinking of is a canalised river running through a city, with a rectangular cross-section whose depth is a significant proportion of its width.
Thank you all very much for the thoughtful answers. The consensus answer is that it is possible, and a number of you have pointed out that it must obviously be the case or the water would not flow at all. I am convinced, and I appreciate the various insights. It is counterintuitive for me but maybe not at all surprising for others.
This implies (assuming steady state and leaving aside level changes over time) that the level of the Thames at London Bridge must be higher than that at Tower Bridge, despite there being no visible “fall” at any point between the two, and that both are higher than sea level. If the surface of the Thames were to freeze, a marble placed on the frozen surface at London Bridge might be expected to roll downhill to Tower Bridge. I suspect however that the height difference may be imperceptibly small.
I don’t see why the upper surface should be horizontal. There’s going to be some movement of the upper layers of water and that will cause a gradient.
You could artificially constrict the surface to be horizontal by putting a flat barrier just under the surface to prevent any of the upper and lower flow from interacting. But that’s a very different system, and the barrier will act as a restriction. Looking at the lower part, it will still flow because the exit point will have a larger cross-section than the entry point, and so the center-of-mass of any cross-section of water will be falling as it progresses. But the flow resistance is greater, which means that on the source end, the incoming flow will get backed up until it raises the head pressure, which will go up until the steady-state flow is reached.
Still, standing water can have a molecularly smooth surface that reflects light without scattering, but still not be planar, with parts of it sloped. If you hang a powerful magnet over the water, it depresses the water right under the magnet. See the Moses effect:
More thoughts:
This suggests (even more surprisingly to me) that even large lakes such as Lake Erie or Lake Ontario don’t have a horizontal surface - the average elevation at the western “inflow” end must be higher than that at the “outflow” end. Is this effect measurable?
