If I remember correctly, the frequency of microwaves used to cook food causes water molecules to rotate. This increases their kinetic energy, thus increasing the temperature of the food. I just thought that was somehow related to his discussion of vortices with diameter smaller than "L" (I think the width of a water molecule can be considered very small). There's a very well known phenomenon in Chemistry called superheating, in which pure water can be heated over 100° C without actually boiling. This is because the water doesn't have impurities around which to form a nucleation center for steam bubbles. A simple jolt or other physical disturbance is enough to make the superheated water "explode". It happens all the time in first-year Chemistry labs. :) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-pgUWQgJ1TbY.html
I notice that in his 'cheating' example, the original whorl creates another which is turning in the same direction, and then that one creates the third which is also turning in the same direction. Wouldn't the real case always create ancillary whorls which rotate in the opposite direction, which causes the distribution component to grow in such a way that it directly opposes the increase in velocity of the original? The viscosity should cause something which is rotating clockwise to force adjacent regions to rotate counter-clockwise and therefore make the third whorl as impossible as a set of 3 interlocked gears? Actually, there are 3-gear systems now using an interesting sort of radial design (3 dimensional gears, I don't know if they can even work in 2 dimensions), perhaps water could (theoretically) be configured to move in a pattern like those gears, rather than the sort of standard 2D gear-like whorls depicted?
@Kelvin I find it hard to believe you honestly don't understand how metaphors work. What magic in vortices permits propagation of rotational forces in the same direction regardless of opposition?
do you mean ''behind the event horizon''? You can't use such loose terms as ''in a black hole'' when it talking about black holes, you have to be mathematically precise.
The reason why the mathematical analysis has to be done via fluids, is because the physical evidence of identifiably mathematical-elemental information is the Planck Dimension, for which the related mathematical model is the generality of the wave equation's functional point probability recognition, .dt, infinitesimal instant, is at least a conceptual equivalent to the eternal relationship of a "liquid" multi-oscillator or angle-space orientation of singularity. Or, in alternate/complimentary time and space nomenclature, the general principle of universal phase connection is Quantum, and Navier-Stokes combined with the occurrence of quantized information-liquidity of Primes, in an infinite 1-0D interval, is the cause-consequence implied dynamical function of temporal superposition. So, Reflection-Rotation in Duration implies a "leaky" durability of a p-brane, which is a transverse-tangential conic-harmonic spatial structure projected "from", or inflated by, the singularity, ..universal vanishing point p. It's a spongiform quantum foam of infinite complexity held together by eternal existence and inflated by proportionate uncertainty flowing through the conglomeration of prime-bubbles. So the process is a matter of "Surmise" or opinion, that connection is equivalent to instantaneous superposition, is equivalent to tangentially distributed transverse eternal probability, because unity-connection is the single occurrence of universal existence in an infinite superimposed probability state. (With the observable characteristics of the Big Bang theory)
It is a shame that Prof. Tao is claiming that the Navier-Stokes Equations belong to Physics. These important equations is the creation of Engineers, Mathematicians, both ones founded a discipline very far from Physics which is the well-known Classical Mechanics.
there is one error in the beginning.. I may be too much precise but Tao said incompressible fluid but there not exist such a thing in real life, instead he should have said incompressible flow...that is correct, I would not expect such an error from a fields medalist
Although all fluids (including liquids) have some compressibility as you state, it can be assumed they are incompressible for analytical purposes and the results are close enough. There are limits to this assumption.
get out of it it is not your country to make an academy in it you should call it "The Palestine Academy of Sciences and Humanities" instead and you should celebrate Einstein's death but not make an annual memorial lecture for him it is PALESTINE فلسطين
