The reason the stroll number should be similar for flying and swimming animals is because there's a difference in velocity and density of the material they're flying through. So I would imagine the velocity of any swimming animal is dramatically slower than the average velocity of a flying animal.
I'm trying to figure out is if this number captures the effect of the circular rotation in the vortices that the wings create which actually store energy and if the wing or the animal can retain contact with those vortices for long a period as possible that can use less energy to create the next vortices and use the stored energy in the vortices to either move forward or retain lift. This is why double winged creatures like dragonflies and bumblebees can fly sufficiently because their second Wing is operating within the stored energy of the vortices that the first one created thus it is not pushing on still air but is pushing on hopefully the opposite uplifting rotation of the tail end of the vortices the first one created. This is why bumblebees which shouldn't be able to fly without such effects of vortices can fly their large bodies with very small wings. Each Wing is not creating the energy anew each time. It's basically like flying at the edge of a tornado. If your first Wing created the tornado it took a lot of energy to get all that air spinning and if your second Wing can then push against the edge of the tornado the first one created then the second Wing is recapturing a lot of that energy.
It's unclear to me whether the stroll number really recognizes the energy and the vortices it may in a passive way but it'd be interesting if there was some measurement or number that actually measured the speed and circumference of vortices and how long an animal stayed within the proximity of the vortices it made when swimming or flying.
Yes Reynolds number is in the numerator, the denominator is the bulk flow speed. Because the numerator includes the local flow acceleration you have to include the characteristic length and with it the Reynolds number.
You are correct with vortices storing energy, when a bird takes off it creates a huge vortex sheet, and with their adjustable wings they are able to position them to take maximum effect of the laminar flow layer caused by the vortex.
Trout can swim upstream because again they position their bodies so that their scales take advantage of the forward thrust caused by vortex recirculation.
Also birds and fish have similar Reynolds number because of the speed and density differences put their Reynolds numbers in roughly the same range.(kind of how the moon and sun look the same size from our POV even though they're not)
Fish have scales and birds have feathers which alter the characteristic length and in turn the Reynolds number. The lower the Reynolds number the lower the probability of turbulence, and since it's part of the numerator, lowering RE# also lowers Strouhal number, for a given bulk flow speed.
Thanks for the explanation.
I know the fish story but didn't know the involvement of their scales. Makes sense.
Thanks for the interaction.
It was an interesting post. Thank you.
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