In light of the recent Navier-Stokes discussions, I find it important to bring attention to the real-world constraints involved. A literal singularity where fluid accelerates to an infinite velocity cannot happen in the physical world. Nature's "safeguard" preventing this is that fluids aren't continuous mathematical sheets. They are made of discrete atoms and molecules.As a vortex shrinks to molecular scales, the fluid starts acting like individual molecules bouncing off each other, not like a perfectly smooth liquid body. Energy begins to bleed back into the environment due to factors like thermal fluctuation and electron degeneracy pressure.Navier-Stokes equations treat fluids like an infinitely divisible, continuous gel. When they predict infinite velocity/gradients, it just means that the continuum approximation has broken down. It doesn't suddenly mean there are ways to hack reality. The universal speed limit c, which is now widely known, would completely prohibit infinite velocity from ever being reached.What's really going on is that pure mathematicians are checking for a weak point in the equations. It's a test of whether the 19th century ruleset breaks down at the edge cases. This considers the abstract logic of the ruleset, yet excludes real-world physics constraints from bailing it out.There's no free lunch. That would be shear craziness
>>17052127are you a bot or did you write this post just for the pun in the last sentence?NS not perfectly modeling fluids is trivially true, nobody is surprised by that.mathematicians didnt care for NS because they cared about fluid dynamics or limits of physical models, they care about it because they like studying PDEs
>>17052127I mean aren't tornados and hurricanes real world examples of blowup? Of course in reality there is other factors from preventing it from truly blowing up the universe like you said.
>>17052225Cope
>>17052127I read science magazine summaryThe first thing I thought is there should be bubbles. If there can't be bubbles because the container is full, then the container should break. It reminds me of something like V=IR but what if R is 0, wow the current is infinite with even a small voltageThen it's about the velocity of the fluid, and not the flow rate, so what is the flow rate of the infinite speed whorl?Must be that the cross sectional area of the flow approaches 0 as the velocity approaches infinity, so if you slow it down, maybe you can get a non zero flow that can water jet cut something
>>17052127I see what you did there :D
>>17052127Totally agree. The Solution does not model reality..
>>17052385You stumbled onto how superconductors work! Critical current density states that forcing too much current when R=0 leads the magnetic field to destroy the system.On the other hand, trying to maintain a real liquid at extreme velocity within that cross section would require an insanely strong system to just hold that whorl together. It would just take more energy than one could even hope to extract from it.
>>17052412That's great, hopefully you'd be able to make a +1 whorl and a -0.9 whorl in the opposite direction at the same time and extract 0.1 whorl energy and it would cost less than 0.1 whorl to do it, even if it was 0.09 whorl, you could get 0.01 whorl profit and do it repeatedly
