[mohdbilal131]

I was reading this book by Richard Feynman (6 easy pieces) in which he said that turbulence is one of the unsolved problems of classical mechanics. So has any scientist ever tried to develop a quantum theory in order to explain turbulence?

[sbaffini]

I think that, when referring to "one of the unsolved problems in classical mechanics", it is usually intended that the "mathematical problem known as 3D Navier-Stokes equations" still lacks a proof of existence and unicity (or lack of) for a solution under all but the most trivial circumstances (ridicolously low Re numbers and simple b.c. settings).

Moreover, while the physics of fluids in general is well understood (conservation of mass, momentum, etc.), specific flow mechanisms at play in specific settings may actually not and, again, besides the most trivial cases, we need expeirments (physical or numerical) to investigate them.

Among these, i can rememeber of cases where the quantum nature of the matter assumes a relevant role. Try, maybe, looking in the book of Landau and Lifshitz (the first guess coming to my mind).

In conclusion, it is not the fluid mechanics formulation of the turbulence the real problem (as numerical simulation based on the classical Navier-Stokes equations are known to fit the experimental evidence) as much as understanding the problem itself in the present formulation. Navier-stokes equations are already derived from particle theories without problems and i don't think that going down toward more fundamental physics aspects would add anything new.

Of course, this does not exclude tha a talented physician might see something in the fluid mechanics problem expressed at the quantum level which is instead not as much clear at the "classical level".

[truffaldino]

Originally Posted by mohdbilal131

I was reading this book by Richard Feynman (6 easy pieces) in which he said that turbulence is one of the unsolved problems of classical mechanics. So has any scientist ever tried to develop a quantum theory in order to explain turbulence?

There are tons of works by people from quantum field theory on 2d turbulence. Recent developments include connection between conformal field theory and 2d turbulence, schram-loewner evolution and 2d turbulence etc.

You can see eg related works of this guy

http://www.princeton.edu/physics/peo...netid=polyakov

or this guy

https://www.weizmann.ac.il/home/fnfal/

Also there were a lot of work on renormalization group and turbulence in different dimensions (starting from burgers turbulence in 1d up to conventional 3d) etc.