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Near my house there is a mall that have a cascade, which has a pratically constant flow, and doesn't seem to have perturbations (at least near the edge where water falls), between its two levels.

What botters me is thar that laminar flow that seem unperturbed, break in the middle after falling for a height of approximately 1.1m (it falls another 0.5m, before being colected by a pool, and, I think, repumped up). I don't know exactly how to explain that behavior but I think it must have to do with waves propagating on that filament of water and that make it break after falling a height $h$. Part of that flow is directed forward, and part is directed backwards (see the front view of the sketch below). From this view I can conclude also that there is a perfect left-right simetry (in relation to the vertical red line).

Update1:

I incluided also what I expect from the velocity vectors due to viscosity (with purple arrows on the sketch), similar of what we can see on Flow velocities due to viscosity of the Laminar flow text. Unfortunately I don't have a real picture, or vídeo, of the local.


What is causing this effect? How can it be explained?


Cascade Views - Sketch

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  • $\begingroup$ @Your PS: I think your drawings are terrific! $\endgroup$
    – Michiel
    Commented May 25, 2014 at 7:45
  • $\begingroup$ I would like to see a picture though :) $\endgroup$
    – Bernhard
    Commented May 25, 2014 at 7:55
  • $\begingroup$ @Michiel: I was not expecting a compliment, ty... I made a great effort using my paint skills :) . I hope I made myself clear... $\endgroup$
    – Claudia
    Commented May 25, 2014 at 20:26
  • $\begingroup$ @Bernhard: I am trying to provide a picture, then I will update the post.. $\endgroup$
    – Claudia
    Commented May 25, 2014 at 20:27

2 Answers 2

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As you indicate in your drawing, the velocity of the water is not homogeneous in the spanwise direction: because of inflow conditions, and also because of the friction with air, which will vary as an air circulation is created around the fall. Thus there are gradients of velocity in the system.

Because the water is in free fall, it is accelerated. At some height, a threshold is reached above which the flow becomes turbulent: the shear profiles destabilize. It is of course in the direction normal to the liquid sheet thats this shows most. And because of momentum conservation, you'll have an approximately equal mass of water going to the front and back of the sheet.

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  • $\begingroup$ But why would it be two streams, and not just a whole lot of them? $\endgroup$
    – Bernhard
    Commented May 26, 2014 at 18:23
  • $\begingroup$ First, I am pretty convinced it could be a whole lot of them, but the flow rate was adjusted so as to get something looking good. Second, imagine you have something wavy in the $x,y$ plane: say $x$ is the span direction, $y=\sin(kx)$. Then the "stretch" is higher when $y$ is close to zero deviation, and lower when $y$ is greater (positive or negative), and the flow is even less stable with this stretch. This probably contributes to the fact that the "stretched" part atomizes, part of it going in erratic droplets and part joining the main streams. $\endgroup$
    – Joce
    Commented May 27, 2014 at 6:50
  • $\begingroup$ @Joce: Thanks for the answer... I really believe that some inhomogeneities on the system may lead to that turbulent profile, but still isn't clear for me how they are driven and if those gradients on the velocity would also contribute. I think that what I am really after is to know if we could predict that behavior and determine the height in which this destabilizement occur. $\endgroup$
    – Claudia
    Commented May 31, 2014 at 21:30
  • $\begingroup$ @Claudia: You can read about transition in the wikipedia article en.wikipedia.org/wiki/Laminar-turbulent_transition . There is no general result that can be abstracted from the precise geometry and inflow conditions, and here I am of the opinion that the interaction with air flow also plays a role. I mentioned it and the gradients of velocity present at inlet because they are most likely the origin of the shear flow that will destabilize once the Reynolds number is large enough. $\endgroup$
    – Joce
    Commented Jun 2, 2014 at 12:04
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I think that the water in the sides of the cascade are denser than the middle because the water sources are closer to there. The sides begin to expand. The expansion of the sides sucks water from the middle (the density of the middle allows the expansion of the sides to take affect more rapidly outward) and the cascade parts.

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  • $\begingroup$ thanks for the answer. I don't think there's any change in density...I would only expect greater velocity of the water in the middle, and in the up part of the fillet of water (the front part when falling), due to viscosity. See for example, flow with viscosity of the following text: Laminar flow. $\endgroup$
    – Claudia
    Commented May 25, 2014 at 20:20

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