One of my friends told me that if you shake up a round bottle of vodka that a tornado will form inside. That tornado can tell you if the vodka is good or bad. If the tornado is nice and tight then the vodka is good, but if the tornado is loose then the vodka is bad.
So we set off to the neighborhood liquor store. The result were inconclusive. Not everyone could shake a tornado out of some bottles. One kid got a good tornado inside of a $7.99 bottle of Georgi vodka. I could not get the same results. Also, bottles of Absolute and Finlandia vodka were not producing any tornados.
Looking strictly at the fluid dynamics, I don’t think you can look at a vortex formed in a bottle by shaking it and tell anything about the quality of the vodka. Different vodkas might differ slightly in density and viscosity, which will affect vortex formation, but you’d have to have very controlled conditions to tell the difference. As you indicated, most of the difference will have to do with a person’s shaking technique, and you should be able to generate different types of vortices in the same bottle with different types of shaking.
I think the best way to tell the quality of the vodka by shaking the bottle is that the store owner will likely rap you upside the head when you shake the good stuff and tell you to go play with the cheap bottles.
You CAN, however, make judgements about the proof of the booze by shaking it and observing the bubbles.
IIRC, a higher proof has a higher surface tension and will hold bubbles longer and produce smaller bubbles than a lower proof. This was demonstrated once for me with untaxed corn liquor in a fruit jars. He called it “holding a bead.” The “IIRC” part comes from what came next, which was the taste test, and things got a bit fuzzy after that.
In the case of the store-bought stuff, it is a lot easier just to read the label, though
Me either. And I used ‘apparent’ because quality is pretty subjective. The makers of Grey Goose/Chopin/Ketal vodka would probably say that the quality of home filtered vodka is not improved and that it’s all a trick/illusion/scam, etc. Thus ‘apparent’.