I would premit that I am not an expert (just an enthusiast) and my mathematical background is limited. That said I am trying to figure it out if the effect of coriolis force of big system (our planet for example) has an effect even at microscopic scale, assuming there is no friction or other interaction inside the fluid (eg no polar interaction). My gut feeling was that what matter is the difference in angular velocity of the observed fluids, so if the scale is really small (compared to the system) the difference in angular velocity should be negletable and so the coriolis force. I am dubious about that because coriolis force appear on earth even at small scale, like a sink.. so I was wondering what I am missing
Derek Muller and Destin Sandler had a collaboration where they set out to replicate an experimental setup designed to elicit terrestrial coriolis effect at small scale.
On their respective hemispheres they set up a kiddy pool, less than a foot high high and with diameter of 5 feet or so. When filling the water was directed to flow such that it flowed counter to what you would expect to develop when you start draining the pool. Then the water in the pool was left undisturbed for a day to allow any residual current from filling to come to a standstill.
Then a valve was opened, allowing the water to drain via an opening in the center. Over time the flow of the water towards the drain started to rotate with respect to the pool.
What Muller and Sandler did was a demonstration rather than an experiment. As far as I can tell they each did only one run.
It cannot be excluded that the bottom of the kiddy pool had bumps or folds that affected the flow of the water.
Anyway, this type of experiment has been done in the past, with much better elimination of possible sources of bias, and it has been shown that if you are careful enough then even at small scale the effect can be elicited consistently.
... coriolis force appear on earth even at small scale, like a sink ...
The idea that the Coriolis force determines whether a sink or bathtub drains clockwise or anti-clockwise is a misconception. On such a small scale, the Coriolis force due to the Earth’s rotation is negligible, and the direction of draining is determined by asymmetries in the geometry of the sink or bathtub.