In fluid mechanics…
Leave now. …
Despite the uncertainties principle of the mathematicians such as Reynolds et al, fluid mechanics is no more complex than a fairground charade. You put a coin in the slot and a one armed bandit takes it off you.
Apart from obvious scams such as the "free toy" crane and the modern computer games of chance, the old fashioned penny in the slot machine was a form of gambling that relied on simple fluid physics. You put a penny in the slot and a bagatelle dropped a ball for you to practice ballistics.
Obviously the machines were mass produced and the springs and mazes could be doctored; but a sufficiently penny supplied addict could soon accomplish the feat of getting his coin back for another go on selected machines.
Not so simple was the machine loaded with pennies that allowed the fool to add to the pile hoping to tip it over. That was a 3D pyramid with the physics loaded to the power of X^cubed. Few losers could play them successfully before becoming wise enough to stop before his supply ran out.
Fluid mechanics in a simple reservoir where the liquids are mobile, require only that the observer is aware that the interaction of the contents of the reservoir are subject to action among layers as numerous as the layers of an onion.
The outer layer is connected to the walls of the reservoir. The next layer is tied to the reaction of the outer layer's reaction to the movement of the total mass of fluid and the wall of the container.
The next layer requires only that the observer know that the interaction depends on the interaction of the outer layer to the movement of the total mass of fluid and the wall of the container and the reaction of the intervening layer to the…
From this you can see that syllogy will provide for the fastest stream layer to be in the centre of a simple tube. A stream surface in an open reservoir will allow the weakest layer to combine the overall velocity of all the layers to appear on the least restrictive surface.
This is the open air in the real world. The center of a stream surface near the mouth of a river is usually the fastest flowing current in the whole system.
I suppose this doesn't include waterfalls which traditionally take place upstream.
With particulates, motion is usually in the trajectory = Downhill +water pressure -side to side stirring.
So how do boulders jump?
Leaving aside the fact that streams erode their containers and thus change their trajectories….
Oh, forget all that.
Jumping takes place with Newton's laws of motion. They go in a straight line until forced to go around. They tend to go around according to the laws of least resistance. Jumping up is easier than carving chunks out of any reservoir.
And that is why boulders jump.
Except for the interference of counter currents of course.
Enter stage right: mysterious numbers.
When there is a blockage however minor in the system, things build up towards criticality. As the boulder resists motion being some 5.5 times heavier than water and requiring, then 5.5 times more water behind it to accelerate it to the same velocity of the stream, water backs up behind it and climbs over it.
(Of course there is a certain amount of backlash too when the boulder crashes back down pushing water below it out of the way. Not as much as 5.5 times its velocity or whatever but it may be more if the water is deep. The boulder displaces its own volume incrementally…..)
Water climbing over it offers lift from the same principle of aerodynamics that cause flight. Boulders trees and tyres, old TV sets and shopping trolleys are not particularly good airfoils so the physics of jets and water through smaller pipes etc applies.
I am not suggesting you get involved with trying to understand the maths. Far from it. I can't understand it myself. But it is good to know that others can (or since I can't say for sure) tried to.