Taking a cat-nap?
<snip>
Done. All that because you don't see that the flow must go
with the belt. Patently obvious.
But humber, with respect, I have tried several times to clarify this point about the boundary layer, and you keep evading the question. For those of us who believe in the equivalence of these situations, it is like this:
Yes, the boundary layer goes with the belt - it has to and that is obvious. But, because we are discussing velocities w.r.t. the belt, that velocity of the b.l flow is slower than the surface itself. Hence, for a molecule of the actual treamill belt, looking up, all it sees is molecules of air that it's trying to grab and push along with it, but because it's not a solid, they are slipping behind. Thus, from the frame of reference of the belt, the air is either "going with it" completely (i.e. would be measured as stationary in that frame), or is going
left to right w.r.t. it.
[ETA: had to reverse
that myself then!]
This then means that anything going at the same speed as the belt, like your rabbit, does not see or feel the boundary layer going with the belt faster than the belt. To go back to my scenario, the person on the belt facing backwards, feels the air down their back at all heights, and the speed of that wind on their backs is exactly the same as it would be if they stood still on an equivalent surface (or the very same surface if you like) in "real wind".
Look. You wanted to solve this BL problem a long time ago, and that's what I was trying to do. It's quite simple. Answer these questions:
1. Do you mean that the boundary layer goes in the direction of the belt
faster than the belt? Y/N
2. If the answer to 1. is No, then, when you're on the belt going with the belt, at belt speed, is the BL going to overtake you?
3. If the answer to 1. is Yes, how does a belt accelerate still air to go faster than it?
These depend on you being able to visualise things from different speeds, i.e. frames of reference, or be able to do the maths for that correctly, or be willing to test the hypothesis empirically, none of which seem to pertain in your case at any kind of reliable level. If you don't like the above examples, there is the other I suggested. Stick a "ladder" to a large piece of card, with very light pieces of tissue paper stuck to the rungs. Wave it through the air so that the card slices the air like the surface of a treadmill, and the tissue catches the still air in the room. Is there any level from top to bottom where the paper swings forwards? If not, what does it mean to say that the direction of the BL is reversed? They all blow backwards. If you stop that and put it down and blow it with a hairdryer, they blow 'backwards' (downwind) as well.
Or answer my question about how the air over a car in a windtunnel (still surface, "real wind") should all go in the same direction, but when the car drives off down the street in still air, the BL goes the wrong way, according to what you seem to be saying?
And I'm sorry to burst your bubble, but the diagram above is not "clarity". You don't specify what the figures are measured in relation to, which is precisely the point. And if I interpret them as best I can, there are glaring errors...not only are things from different frames of reference, but the BL shown going R-L over the treadmill (which is the right direction relative to the experimenter's ground, the room) should be 4, not 6, as has been explained to you by several people, including me. If the BL we chose to measure in the real wind was slowed to 1 m/s (closer to the ground than the layer going at 6), then in the treadmill situation that would have to be going 9 m/s right to left w.r.t. the room. How could it be going 1 m/s, with the belt, dragged by the belt, yet air above dragged by the belt with the belt faster than that? The belt drags the air right next to it to 10 m/s, not zero.
And just look at it - in the bottom left diagram, you've got "10 m/s ---->" written three times down the left hand side. What the hell
are they? It's anybody's guess.