Renormalization in Fluidodynamics

[random3f]

During a lecture about QFT (http://video.google.it/videoplay?docid=-8230150359736309141&ei=xFWDSNSiDITgjAKz46i3Bg&hl=it" ) Alain Connes said that Green (in1850) used a mass renormalization to calculate the acceleration of a ball in a liquid, because you can't directly calculate it just using Archimede's Law. I didn't understand It very well. So does anybody know a reference or where to find this kind of calculation?

Thank you.

 

[Zacku]

During a lecture about QFT (http://video.google.it/videoplay?docid=-8230150359736309141&ei=xFWDSNSiDITgjAKz46i3Bg&hl=it" ) Alain Connes said that Green (in1850) used a mass renormalization to calculate the acceleration of a ball in a liquid, because you can't directly calculate it just using Archimede's Law. I didn't understand It very well. So does anybody know a reference or where to find this kind of calculation?

Thank you.

Hello,

I don't know where to find such a calculation but I can explain the reason why it has to be done. Actually Connes talks about a ping pong ball that would be immerged into water because we are holding it for example and then we let it go. The archimede's law applies then and the ball feels a strength that repels it to the surface of water.
The fact is that when you try to compute the acceleration by applying Newton's law F=ma, you don't find the experimental result. The reason is that, when an object is moving in a fluid it induces hydrodynamics currents around itself which modify, in an effective way, the ball inertia in Newton's law. I will try to find a more quantitative reference in the next few days...

P.S : excuse me for my english

 

[denian]

Renormalization is a powerful tool in fluid dynamics that allows us to understand and model complex systems at different scales. In the lecture by Alain Connes, he mentioned that Green used mass renormalization to calculate the acceleration of a ball in a liquid. This refers to the process of adjusting the mass of an object in order to account for the effects of the surrounding fluid.

In fluid dynamics, we often encounter situations where the properties of the fluid, such as viscosity and density, affect the motion of objects within it. This can make it difficult to accurately calculate the motion of an object using basic principles such as Archimedes' Law, which only takes into account the weight of the object and the buoyant force of the fluid.

By using mass renormalization, we can adjust the mass of the object in order to incorporate the effects of the fluid on its motion. This allows us to more accurately predict the acceleration of the object and understand the overall behavior of the system.

To learn more about this concept, I recommend looking into the work of Leonhard Euler and Daniel Bernoulli, who were pioneers in the field of fluid dynamics and developed many of the foundational principles that are still used today. Additionally, textbooks on fluid dynamics and hydrodynamics may also contain examples and explanations of mass renormalization in various contexts.