# If the top layer of a large river freezes, is the remainder's rate of flow affected?

This question is a hypothetical, and has to do with the notion of cheap, modular turbines that can be sunk and anchored to a specific depth in a body of water. Each would not generate much power, but collectively that might be different, and it's a possible means of giving people living on riverfront properties greater self sufficiency. But that's not the question, just the context, so it need not be addressed.

The question is: When the topmost layer of a large body of moving water freezes, and assuming the water beneath is insulated by the ice and does not freeze, does that remaining water's rate of flow (rate, not volume) differ from its rate when none of the body of water was frozen?

• More or less it would, it shields off wind (depending on the wind direction it can accelerate or deccelerate the flow of water) and I would argue the ice may lubricate and retain the kinetic energy of the flowing water which might otherwise dissipate to the air. Jan 18, 2020 at 23:31
• I think shearing along the ice layer would induce a velocity gradient, as it does along the riverbed. So you'd have 2 zero velocity points (base and top of flow) instead of one. It's just a guess, I'm more familiar with lava flows, but this principle is valid for all newtonian fluids. Jan 19, 2020 at 10:46
• I'll bet that somebody somewhere has done a study on this, and that's the type of answer you should be looking for. Jan 19, 2020 at 14:46

## 1 Answer

No, the rate of flow would usually be unaffected. The same volume of water has to get to the sea, so unless the ice was so thick and so well anchored to the riverbank as to exert pressure on the flow of water beneath, which is very unlikely, the rate of flow would remain the same. If, in the unlikely event that the ice exerted pressure on the water, the rate of flow would speed up.

It's the same when you pinch the end of a garden hose. The same volume of water has to get through a narrower opening, so the jet becomes smaller but faster and more powerful because it is under pressure. For your purposes a faster flow would help your turbines to do their job but as I say, icing conditions are rarely such that ice would exert pressure on the flow. The friction between the current and the relatively thin coating of ice which usually occurs would not be enough to have any noticeable effect on the rate of flow.

• This seems like a sensible answer in general, but I'd love to see a citation for the last part. Is there a reason that the boundary with the ice shouldn't have as much, or nearly as much, effect as the boundaries with the banks and the riverbed? Jan 19, 2020 at 21:27
• There is much less friction with ice than with the river bed. To test that, get a pair of ice skates and go skating on the river in mid winter. There will be hardly any friction. Next, wait till there is a summer drought and go skating on the river bed. You'll find there is far more friction. It could also happen that after the ice forms, the volume of flow decreases slightly so that the water doesn't even touch the ice, though it is still pressed hard against the river bed. Jan 19, 2020 at 21:54
• From a quick Google Scholar search, it looks as though the resistance from a smooth sheet of ice is around 1/5 to 1/10 of that from a smooth seabed. However, it's rarely smooth, and all sorts of complex stuff seems to happen when there's an ice dam intruding into the flow from the surface, drastically reducing the vertical extent of the flow. I'm not going to try an answer, as I don't understand it well enough. Jan 20, 2020 at 9:46
• I would intuitively think friction with the open air (if it doesn't blow in the same direction) would even be larger than with ice. Riverbanks sometimes are very rough and can even have lateral capillary flow. However, I don't think even river banks cause that much of resistance to water flow if the river is wide and deep enough. These are just my intuition. Jan 21, 2020 at 22:23